c
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c       This is the end of the debugging code and the beginning
c       of the interpolation on the triangles routines
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c       
c     ortho2smexps  - constructs (or rather retrieves) the
c         gaussian-like interpolation nodes and weights for the polynomials 
c         (i.e. smooth functions) 
c         on the standard triangle with the vertices
c         (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3)) (up to order 20)
c
c     ortho2sfexps  - constructs (or rather retrieves) the
c         chebychev-like interpolation nodes and weights for the polynomials 
c         (i.e. smooth functions) 
c         on the standard triangle with the vertices
c         (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3)) (up to order 20)
c
c     ortho2siexps  - constructs (or rather retrieves) the
c         gaussian-like interpolation nodes and weights for the polynomials 
c         (i.e. smooth functions) 
c         on the simplex triangle with the vertices
c         (0,0), (1,0), (0,1)    (up to order 20)
c
c     ortho2intpmatr - form the interpolation matrices on the nodes
c       (xs,ys). The nodes are located on the standard triangle with the
c       vertices (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))
c
c     ortho2diffmatr - constructs the matrices of spectral differentiation 
c       on the nodes (xs,ys). The nodes are located on the standard triangle 
c       with the vertices (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))
c
c     ortho2sipols - evaluates a bunch of orthogonal polynomials on
c         the simplex at the user-provided point
c
c     ortho2sipolders - evaluates a bunch of orthogonal polynomials on
c         the simplex at the user-provided point, and the derivatives of the
c         said polynomials
c
c     ortho2siexevc - evaluate the value of polynomial expansion on the simplex
c          at the user-provided point (complex *16 version)
c
c     ortho2triangle - construct triangles: simplex and standard
c
c     ortho2_stdtosimplex - map the standard triangle to the simplex
c     ortho2_simplextostd - map the simplex triangle to the standard 
c
c
c
        subroutine ortho2smexps(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
        implicit real *8 (a-h,o-z)
        dimension xs0(1),ys0(1),ws0(1)
        dimension xs1(3),ys1(3),ws1(3)
        dimension xs2(6),ys2(6),ws2(6)
        dimension xs3(10),ys3(10),ws3(10)
        dimension xs4(15),ys4(15),ws4(15)
        dimension xs5(21),ys5(21),ws5(21)
        dimension xs6(28),ys6(28),ws6(28)
        dimension xs7(36),ys7(36),ws7(36)
        dimension xs8(45),ys8(45),ws8(45)
        dimension xs9(55),ys9(55),ws9(55)
        dimension xs10(66),ys10(66),ws10(66)
        dimension xs11(78),ys11(78),ws11(78)
        dimension xs12(91),ys12(91),ws12(91)
        dimension xs13(105),ys13(105),ws13(105)
        dimension xs14(120),ys14(120),ws14(120)
        dimension xs15(136),ys15(136),ws15(136)
        dimension xs16(153),ys16(153),ws16(153)
        dimension xs17(171),ys17(171),ws17(171)
        dimension xs18(190),ys18(190),ws18(190)
        dimension xs19(210),ys19(210),ws19(210)
        dimension xs20(231),ys20(231),ws20(231)
        dimension xsout(1),ysout(1),wsout(1),umatr(1),vmatr(1)
c
c       This subroutine constructs (or rather retrieves) the
c       interpolation nodes for the polynomials (i.e. smooth functions)
c       on the standard triangle with the vertices
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))            (1)
c
c       and the corresponding quadrature weights. It also constructs the
c       matrix vmatr converting the coefficients of the polynomial
c       expansion to its values at the interpolation nodes, and its
c       inverse umatr, converting the values of a function at the
c       interpolation nodes into the coefficients of the polynomial
c       expansion.
c
c       The nodes are fully symmetric and the corresponding quadrature
c       weigths are positive. The quadrature is of high order but it
c       does NOT integrate the pairwise products (user beware).
c
c       The quadrature orders correspond to the ones in the tables given
c       by Bogdan Vioreanu (see Yale technical report TR-1443). 
c       http://www.cs.yale.edu/publications/techreports/tr1443.pdf
c
c       Note that in Vioreanu's tables, orders 5,6,9,12 are rotationally
c       symmetric only, which gives one extra order for integration and
c       better interpolation conditioning. Also note, that the tables
c       have been re-generated independently, so the nodes and weights may
c       be different.
c
c       The tables are valid up to order 20.
c
c       NOTE #1: the nodes are fully symmetric for all orders
c
c       NOTE #2: the nodes are gaussian-like, i.e. they attempt to integrate
c       higher polynomial orders. 
c
c
c interp    0     1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------------
c quadr     1     2     4     5     7     8    10    12    14    15    17
c  -----------------------------------------------------------------------
c nodes     1     3     6    10    15    21    28    36    45    55    66
c  -----------------------------------------------------------------------
c cond #   1.0   1.0   1.4   1.9   2.1   3.4   4.3   4.8   4.8   6.5   8.1  
c
c
c interp   11    12    13    14    15    16    17    18    19    20
c  -----------------------------------------------------------------------
c quadr    19    20    22    24    25    27    28    30    32    33
c  -----------------------------------------------------------------------
c nodes    78    91   105   120   136   153   171   190   210   231
c  -----------------------------------------------------------------------
c cond #  15.7  19.2  21.4  38.6  31.4  44.3  75.3  117   153   194
c
c       
c       NOTE #3: all weights are positive
c
c       NOTE #4: the nodes are closer to the boundary (but still usable)
c       than chebychev-like ones (see ortho2sfexps)
c
c       NOTE #5: the weights are accurate to 30 digits only
c          (tables are accurate to 14-15 digits for orders 13 and above)
c
c       NOTE #6: compared with ortho2exps2.f, nodes are different for
c           orders 5,6,7,8,9,10,11,12.
c
c       NOTE #7: interpolation condition numbers have not been optimized 
c           (but they are reasonably small)
c
c         Input parameters:
c
c    itype - the type of the calculation to be performed. currently
c          unused
c    norder - the order of the expansion
c
c
c         Output parameters:
c
c    npols - the number of the polynomials, i.e. the terms in the
c          expansion
c    xsout - the x-coordinates of the interpolation nodes (npols of them)
c    ysout - the y-coordinates of the interpolation nodes (npols of them)
c    umatr - the npols*npols matrix, converting the values of the polynomial
c          at the interpolation nodes into the coefficients of its expansion
c    vmatr - the npols*npols matrix, converting the coefficients of 
c          the expansion into its values at the interpolation nodes.
c    wsout - the corresponding quadrature weigths (npols of them)
c
c
c    ... interpolation of order  0 , quadratures of order  1
c                   total number of elements is    1
      data xs0/
     1    0.00000000000000000000000000000000D+00/
      data ys0/
     1    0.00000000000000000000000000000000D+00/
      data ws0/
     1    0.45590141139095552839871265039273D+01/

c    ... interpolation of order  1 , quadratures of order  2
c                   total number of elements is    3
      data xs1/
     1    0.50000000000000000000000000000000D+00,
     2    0.00000000000000000000000000000000D+00,
     3   -0.50000000000000000000000000000000D+00/
      data ys1/
     1   -0.28867513459481288225457439025098D+00,
     2    0.57735026918962576450914878050196D+00,
     3   -0.28867513459481288225457439025098D+00/
      data ws1/
     1    0.15196713713031850946623755013091D+01,
     2    0.15196713713031850946623755013091D+01,
     3    0.15196713713031850946623755013091D+01/

c    ... interpolation of order  2 , quadratures of order  4
c                   total number of elements is    6
      data xs2/
     1    0.00000000000000000000000000000000D+00,
     2   -0.72527135947068776962128560979340D+00,
     3    0.00000000000000000000000000000000D+00,
     4   -0.33784547274789465895498776164916D+00,
     5    0.72527135947068776962128560979340D+00,
     6    0.33784547274789465895498776164916D+00/
      data ys2/
     1    0.83747122925185483484415621413487D+00,
     2   -0.41873561462592741742207810706744D+00,
     3   -0.39011034927098671317419951524681D+00,
     4    0.19505517463549335658709975762341D+00,
     5   -0.41873561462592741742207810706744D+00,
     6    0.19505517463549335658709975762340D+00/
      data ws2/
     1    0.50127155117357779154594371101053D+00,
     2    0.50127155117357779154594371101054D+00,
     3    0.10183998201296073031164317902986D+01,
     4    0.10183998201296073031164317902986D+01,
     5    0.50127155117357779154594371101053D+00,
     6    0.10183998201296073031164317902986D+01/

c    ... interpolation of order  3 , quadratures of order  5
c                   total number of elements is   10
      data xs3/
     1    0.00000000000000000000000000000000D+00,
     2    0.78666101639967696838369807741827D+00,
     3    0.00000000000000000000000000000000D+00,
     4    0.30094676896614446173661526090005D+00,
     5   -0.78666101639967696838369807741827D+00,
     6    0.24288496199708743989786878437904D+00,
     7    0.54383173096323190163448404527909D+00,
     8   -0.24288496199708743989786878437904D+00,
     9   -0.30094676896614446173661526090005D+00,
     *   -0.54383173096323190163448404527909D+00/
      data ys3/
     1    0.00000000000000000000000000000000D+00,
     2   -0.45417894957933810585376535186351D+00,
     3    0.90835789915867621170753070372702D+00,
     4   -0.45421109445661253251431660004936D+00,
     5   -0.45417894957933810585376535186351D+00,
     6    0.48773309433983369328454581322934D+00,
     7   -0.33521999883221160770229213179975D-01,
     8    0.48773309433983369328454581322934D+00,
     9   -0.45421109445661253251431660004936D+00,
     *   -0.33521999883221160770229213179975D-01/
      data ws3/
     1    0.90708593210472630247407787570254D+00,
     2    0.27481272244823141968358523316723D+00,
     3    0.27481272244823141968358523316723D+00,
     4    0.47124833574335578707704882145384D+00,
     5    0.27481272244823141968358523316723D+00,
     6    0.47124833574335578707704882145384D+00,
     7    0.47124833574335578707704882145384D+00,
     8    0.47124833574335578707704882145384D+00,
     9    0.47124833574335578707704882145384D+00,
     *    0.47124833574335578707704882145384D+00/

c    ... interpolation of order  4 , quadratures of order  7
c                   total number of elements is   15
      data xs4/
     1    0.00000000000000000000000000000000D+00,
     2   -0.27344573096654179666874290539477D+00,
     3    0.27344573096654179666874290539477D+00,
     4   -0.42233238215340581924615566001252D+00,
     5    0.42233238215340581924615566001252D+00,
     6    0.00000000000000000000000000000000D+00,
     7   -0.18517708686734435661867105631915D+00,
     8   -0.67031349478008169894818481229504D+00,
     9    0.18517708686734435661867105631914D+00,
     *   -0.48513640791273734232951375597590D+00,
     1    0.67031349478008169894818481229504D+00,
     2    0.48513640791273734232951375597590D+00,
     3    0.00000000000000000000000000000000D+00,
     4   -0.84624076047564449367313431517587D+00,
     5    0.84624076047564449367313431517587D+00/
      data ys4/
     1    0.31574793276457378418547105481567D+00,
     2   -0.15787396638228689209273552740784D+00,
     3   -0.15787396638228689209273552740784D+00,
     4    0.24383371452376474985074290854059D+00,
     5    0.24383371452376474985074290854059D+00,
     6   -0.48766742904752949970148581708119D+00,
     7    0.66709931235482596900014874899532D+00,
     8   -0.17318159475149501708574603496963D+00,
     9    0.66709931235482596900014874899532D+00,
     *   -0.49391771760333095191440271402570D+00,
     1   -0.17318159475149501708574603496963D+00,
     2   -0.49391771760333095191440271402570D+00,
     3    0.97715466171969393506910087330460D+00,
     4   -0.48857733085984696753455043665230D+00,
     5   -0.48857733085984696753455043665230D+00/
      data ws4/
     1    0.57903548483294591423542964237399D+00,
     2    0.57903548483294591423542964237399D+00,
     3    0.57903548483294591423542964237399D+00,
     4    0.29578809508516787711856076890140D+00,
     5    0.29578809508516787711856076890141D+00,
     6    0.29578809508516787711856076890141D+00,
     7    0.24944927325911940024010038068926D+00,
     8    0.24944927325911940024010038068926D+00,
     9    0.24944927325911940024010038068926D+00,
     *    0.24944927325911940024010038068926D+00,
     1    0.24944927325911940024010038068926D+00,
     2    0.24944927325911940024010038068926D+00,
     3    0.14594924486683250282818432865517D+00,
     4    0.14594924486683250282818432865517D+00,
     5    0.14594924486683250282818432865517D+00/

c    ... interpolation of order  5 , quadratures of order  8
c                   total number of elements is   21
      data xs5/
     1    0.41194192657853010982865870129986D+00,
     2   -0.41194192657853010982865870129986D+00,
     3    0.21338599921749440268499811887570D+00,
     4    0.00000000000000000000000000000000D+00,
     5    0.00000000000000000000000000000000D+00,
     6   -0.21338599921749440268499811887570D+00,
     7    0.20857398496582545094850354093101D+00,
     8   -0.20857398496582545094850354093101D+00,
     9    0.54532428466503419131050832984425D+00,
     *   -0.54532428466503419131050832984426D+00,
     1    0.33675029969920874036200478891324D+00,
     2   -0.33675029969920874036200478891324D+00,
     3    0.61651198554323269517089684287530D+00,
     4    0.74641524507499706560581304184834D+00,
     5   -0.61651198554323269517089684287530D+00,
     6   -0.74641524507499706560581304184834D+00,
     7    0.12990325953176437043491619897304D+00,
     8   -0.12990325953176437043491619897303D+00,
     9    0.90578275359714536457244798934681D+00,
     *   -0.90578275359714536457244798934681D+00,
     1    0.00000000000000000000000000000000D+00/
      data ys5/
     1   -0.23783478220060741129500105273301D+00,
     2   -0.23783478220060741129500105273301D+00,
     3    0.12319846408951766613334398575003D+00,
     4   -0.24639692817903533226668797150005D+00,
     5    0.47566956440121482259000210546603D+00,
     6    0.12319846408951766613334398575003D+00,
     7   -0.50926599872802291799663328816150D+00,
     8   -0.50926599872802291799663328816149D+00,
     9    0.74002629815053037096272874649981D-01,
     *    0.74002629815053037096272874649981D-01,
     1    0.43526336891296988090036041351151D+00,
     2    0.43526336891296988090036041351151D+00,
     3   -0.50594272453056402070651247697118D+00,
     4   -0.28094367895274208605804537200598D+00,
     5   -0.50594272453056402070651247697118D+00,
     6   -0.28094367895274208605804537200598D+00,
     7    0.78688640348330610676455784897716D+00,
     8    0.78688640348330610676455784897716D+00,
     9   -0.52295391661663234099806653900769D+00,
     *   -0.52295391661663234099806653900769D+00,
     1    0.10459078332332646819961330780154D+01/
      data ws5/
     1    0.33917974956253817294776592406612D+00,
     2    0.33917974956253817294776592406612D+00,
     3    0.38758245225341608248421340887676D+00,
     4    0.38758245225341608248421340887676D+00,
     5    0.33917974956253817294776592406612D+00,
     6    0.38758245225341608248421340887676D+00,
     7    0.19009947908771557475880531795232D+00,
     8    0.19009947908771557475880531795232D+00,
     9    0.19009947908771557475880531795232D+00,
     *    0.19009947908771557475880531795232D+00,
     1    0.19009947908771557475880531795232D+00,
     2    0.19009947908771557475880531795232D+00,
     3    0.17509278958533358190105932301112D+00,
     4    0.17509278958533358190105932301112D+00,
     5    0.17509278958533358190105932301112D+00,
     6    0.17509278958533358190105932301112D+00,
     7    0.17509278958533358190105932301111D+00,
     8    0.17509278958533358190105932301112D+00,
     9    0.62524632141132525910666886439333D-01,
     *    0.62524632141132525910666886439334D-01,
     1    0.62524632141132525910666886439333D-01/

c    ... interpolation of order  6 , quadratures of order  10
c                   total number of elements is   28
      data xs6/
     1   -0.00000000000000000000000000000000D+00,
     2    0.18198879794064935596162112438012D+00,
     3   -0.18984606011787978345060759355777D+00,
     4   -0.18198879794064935596162112438013D+00,
     5   -0.37183485805852913941222871793789D+00,
     6    0.37183485805852913941222871793789D+00,
     7    0.18984606011787978345060759355777D+00,
     8   -0.45604440912430706100423731491474D+00,
     9    0.45604440912430706100423731491474D+00,
     *   -0.00000000000000000000000000000000D+00,
     1    0.27250079579468194023884839447403D+00,
     2   -0.00000000000000000000000000000000D+00,
     3   -0.27250079579468194023884839447403D+00,
     4   -0.53495344799133098730940442584470D+00,
     5   -0.63663129948675283473474306980112D+00,
     6   -0.36413050369207089449589467532709D+00,
     7    0.63663129948675283473474306980112D+00,
     8    0.53495344799133098730940442584470D+00,
     9    0.36413050369207089449589467532709D+00,
     *    0.98658608416716666569522426444706D-01,
     1   -0.98658608416716666569522426444706D-01,
     2   -0.80715686527894965687110506529034D+00,
     3   -0.70849825686223299030158263884563D+00,
     4    0.80715686527894965687110506529034D+00,
     5    0.70849825686223299030158263884563D+00,
     6    0.00000000000000000000000000000000D+00,
     7   -0.93188007906144489152796614894753D+00,
     8    0.93188007906144489152796614894753D+00/
      data ys6/
     1    0.00000000000000000000000000000000D+00,
     2    0.32428662930782585458826097784001D+00,
     3   -0.31975023687470840225520350665067D+00,
     4    0.32428662930782585458826097784001D+00,
     5   -0.45363924331174523330574711893403D-02,
     6   -0.45363924331174523330574711893396D-02,
     7   -0.31975023687470840225520350665067D+00,
     8    0.26329736237034250583971557607976D+00,
     9    0.26329736237034250583971557607976D+00,
     *   -0.52659472474068501167943115215952D+00,
     1    0.57779009645998915719423059512945D+00,
     2    0.61771103440342682348656306201350D+00,
     3    0.57779009645998915719423059512945D+00,
     4   -0.30885551720171341174328153100675D+00,
     5   -0.52902436520324290549726733485822D-01,
     6   -0.52488765993966486664450386164363D+00,
     7   -0.52902436520324290549726733485822D-01,
     8   -0.30885551720171341174328153100675D+00,
     9   -0.52488765993966486664450386164363D+00,
     *    0.87506389276684691859151236786929D+00,
     1    0.87506389276684691859151236786929D+00,
     2   -0.35209108519252559091506760612381D+00,
     3   -0.52297280757432132767644476174547D+00,
     4   -0.35209108519252559091506760612381D+00,
     5   -0.52297280757432132767644476174547D+00,
     6    0.10760424289971498961504391468917D+01,
     7   -0.53802121449857494807521957344584D+00,
     8   -0.53802121449857494807521957344584D+00/
      data ws6/
     1    0.36844247020518171223852083756008D+00,
     2    0.26982135907071677972322120367243D+00,
     3    0.26982135907071677972322120367243D+00,
     4    0.26982135907071677972322120367243D+00,
     5    0.26982135907071677972322120367243D+00,
     6    0.26982135907071677972322120367244D+00,
     7    0.26982135907071677972322120367243D+00,
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c    ... interpolation of order  7 , quadratures of order  12
c                   total number of elements is   36
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c    ... interpolation of order  8 , quadratures of order  14
c                   total number of elements is   45
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c    ... interpolation of order  9 , quadratures of order  15
c                   total number of elements is   55
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c    ... interpolation of order  10 , quadratures of order  17
c                   total number of elements is   66
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c    ... interpolation of order  11 , quadratures of order  19
c                   total number of elements is   78
      data xs11/
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c                   total number of elements is   91
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c
c    ... interpolation of order 13, quadratures of order 22
c                    total number of elements is  105
c
      data xs13/
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      data ys13/
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c
c    ... interpolation of order 14, quadratures of order 24
c                    total number of elements is  120
c
      data xs14/
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c
c    ... interpolation of order 15, quadratures of order 25
c                    total number of elements is  136
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c
c    ... interpolation of order 16, quadratures of order 27
c                    total number of elements is  153
c
      data xs16/
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      data ws16/
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     *  0.2020717421352824D-02/
c
c    ... interpolation of order 17, quadratures of order 28
c                    total number of elements is  171
c
      data xs17/
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      data ys17/
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c
c    ... interpolation of order 18, quadratures of order 30
c                    total number of elements is  190
c
      data xs18/
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      data ys18/
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c
c    ... interpolation of order 19, quadratures of order 32
c                    total number of elements is  210
c
      data xs19/
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      data ys19/
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      data ws19/
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c
c    ... interpolation of order 20, quadratures of order 33
c                    total number of elements is  231
c
      data xs20/
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      data ys20/
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     6  -.5400068693131663D+00,-.5400068693131668D+00,
     7  -.5401495682144569D+00,-.5399345336172533D+00,
     8  -.5396522014443998D+00,-.5405612265354280D+00,
     9  -.5424575136736226D+00,-.5428318817340073D+00,
     *  -.5457235284284570D+00,-.5516187406229538D+00,
     1  -.5561539929605884D+00,-.5227361820680647D+00,
     2  -.5089671201550916D+00,-.4991232440540148D+00,
     3  -.4931354283326729D+00,-.4912383339473700D+00,
     4  -.4869424187006372D+00,-.4860363569526482D+00,
     5  -.4868782401995252D+00,-.4868607757511374D+00,
     6  -.4865797946183709D+00,-.4868607757511385D+00,
     7  -.4868782401995241D+00,-.4860363569526465D+00,
     8  -.4869424187006456D+00,-.4912383339473802D+00,
     9  -.4931354283326645D+00,-.4991232440540293D+00,
     *  -.5089671201550831D+00,-.5227361820680681D+00,
     1  -.4688605099115074D+00,-.4481438416470861D+00,
     2  -.4329187724571729D+00,-.4228536560699343D+00,
     3  -.4183127122049813D+00,-.4116939608578110D+00,
     4  -.4115698477643141D+00,-.4124379109420533D+00,
     5  -.4118823249283838D+00,-.4118823249283849D+00,
     6  -.4124379109420533D+00,-.4115698477643104D+00,
     7  -.4116939608578204D+00,-.4183127122049968D+00,
     8  -.4228536560699308D+00,-.4329187724571942D+00,
     9  -.4481438416470802D+00,-.4688605099115164D+00,
     *  -.3979244014899689D+00,-.3712930696606194D+00,
     1  -.3488109127414877D+00,-.3344633284617958D+00,
     2  -.3259498462901255D+00,-.3180179905221919D+00,
     3  -.3186536430875911D+00,-.3185811827976662D+00,
     4  -.3178245306767312D+00,-.3185811827976669D+00,
     5  -.3186536430875867D+00,-.3180179905222000D+00,
     6  -.3259498462901397D+00,-.3344633284617967D+00,
     7  -.3488109127415024D+00,-.3712930696606099D+00,
     8  -.3979244014899695D+00,-.3108161793859889D+00,
     9  -.2767761419765814D+00,-.2478348054676549D+00,
     *  -.2298116962132621D+00,-.2174595802410685D+00,
     1  -.2096196967806885D+00,-.2096865420795784D+00,
     2  -.2082986570353376D+00,-.2082986570353375D+00,
     3  -.2096865420795739D+00,-.2096196967806955D+00,
     4  -.2174595802410772D+00,-.2298116962132691D+00,
     5  -.2478348054676646D+00,-.2767761419765742D+00,
     6  -.3108161793859871D+00,-.2093559782736226D+00,
     7  -.1683369282129447D+00,-.1354569710299785D+00,
     8  -.1137081466933807D+00,-.9822888574763560D-01,
     9  -.9016437357888584D-01,-.8760541136035830D-01,
     *  -.8593152545455114D-01,-.8760541136035314D-01,
     1  -.9016437357889154D-01,-.9822888574763482D-01,
     2  -.1137081466933900D+00,-.1354569710299861D+00,
     3  -.1683369282129392D+00,-.2093559782736233D+00,
     4  -.9620155428408154D-01,-.5022464941077820D-01,
     5  -.1498018165525905D-01,0.1061619564178425D-01,
     6  0.2818098072016364D-01,0.3791223243117067D-01,
     7  0.4296576272727459D-01,0.4296576272727975D-01,
     8  0.3791223243116796D-01,0.2818098072017573D-01,
     9  0.1061619564178137D-01,-.1498018165526200D-01,
     *  -.5022464941077290D-01,-.9620155428407889D-01,
     1  0.2585581022425696D-01,0.7475861793924218D-01,
     2  0.1121324408956089D+00,0.1401224068324700D+00,
     3  0.1589122653383552D+00,0.1703864246041710D+00,
     4  0.1752108227207152D+00,0.1703864246041683D+00,
     5  0.1589122653383730D+00,0.1401224068324741D+00,
     6  0.1121324408956088D+00,0.7475861793924232D-01,
     7  0.2585581022426319D-01,0.1539539481658210D+00,
     8  0.2043300266002883D+00,0.2432898973091837D+00,
     9  0.2717599180959087D+00,0.2904002020774888D+00,
     *  0.2998509156584717D+00,0.2998509156584616D+00,
     1  0.2904002020775010D+00,0.2717599180959137D+00,
     2  0.2432898973091847D+00,0.2043300266002816D+00,
     3  0.1539539481658244D+00,0.2851040455224450D+00,
     4  0.3356768427128836D+00,0.3747283348555278D+00,
     5  0.4018217153002729D+00,0.4168825288352260D+00,
     6  0.4192393935613831D+00,0.4168825288352208D+00,
     7  0.4018217153002694D+00,0.3747283348555289D+00,
     8  0.3356768427128787D+00,0.2851040455224459D+00,
     9  0.4162785465333907D+00,0.4653909502752138D+00,
     *  0.5018584218547899D+00,0.5252779944577059D+00,
     1  0.5354775707632690D+00,0.5354775707632673D+00,
     2  0.5252779944576926D+00,0.5018584218547851D+00,
     3  0.4653909502752166D+00,0.4162785465333937D+00,
     4  0.5443796017409231D+00,0.5901591830280281D+00,
     5  0.6214933279826383D+00,0.6415056570710809D+00,
     6  0.6518996925802677D+00,0.6415056570710845D+00,
     7  0.6214933279826273D+00,0.5901591830280319D+00,
     8  0.5443796017409255D+00,0.6663617188598591D+00,
     9  0.7079891296573392D+00,0.7347772241683050D+00,
     *  0.7527760406667792D+00,0.7527760406667957D+00,
     1  0.7347772241683018D+00,0.7079891296573421D+00,
     2  0.6663617188598545D+00,0.7795315908821221D+00,
     3  0.8173373685119958D+00,0.8400492466888745D+00,
     4  0.8457073121398620D+00,0.8400492466888686D+00,
     5  0.8173373685120068D+00,0.7795315908821160D+00,
     6  0.8812690632995090D+00,0.9137505833342268D+00,
     7  0.9260542007898644D+00,0.9260542007898340D+00,
     8  0.9137505833342410D+00,0.8812690632995115D+00,
     9  0.9687016748495727D+00,0.9909757233810908D+00,
     *  0.9982464881080446D+00,0.9909757233810931D+00,
     1  0.9687016748495755D+00,0.1039645977363485D+01,
     2  0.1054690648583530D+01,0.1054690648583550D+01,
     3  0.1039645977363476D+01,0.1094334453366188D+01,
     4  0.1103237481245912D+01,0.1094334453366186D+01,
     5  0.1129451749524257D+01,0.1129451749524257D+01,
     6  0.1144884089780528D+01/
      data ws20/
     1  0.4038074242045579D-03,0.7702153068307685D-03,
     2  0.1981669814506859D-02,0.3202372052766005D-02,
     3  0.4058173986635276D-02,0.5087747133031257D-02,
     4  0.6022218667400390D-02,0.6609045283599506D-02,
     5  0.6956974143949554D-02,0.7214151642671334D-02,
     6  0.7323832578680970D-02,0.7214151642671284D-02,
     7  0.6956974143949440D-02,0.6609045283599518D-02,
     8  0.6022218667400281D-02,0.5087747133030619D-02,
     9  0.4058173986634829D-02,0.3202372052766310D-02,
     *  0.1981669814505755D-02,0.7702153068314371D-03,
     1  0.4038074242045142D-03,0.7702153068313664D-03,
     2  0.3057113443011862D-02,0.5630991961860100D-02,
     3  0.8085787412742301D-02,0.1028616320645236D-01,
     4  0.1287520315340830D-01,0.1465709050187036D-01,
     5  0.1556608416800232D-01,0.1623974204538972D-01,
     6  0.1672692718714403D-01,0.1672692718714431D-01,
     7  0.1623974204539013D-01,0.1556608416800267D-01,
     8  0.1465709050187044D-01,0.1287520315340714D-01,
     9  0.1028616320645137D-01,0.8085787412742877D-02,
     *  0.5630991961858309D-02,0.3057113443011897D-02,
     1  0.7702153068308498D-03,0.1981669814505650D-02,
     2  0.5630991961858400D-02,0.9534654511785980D-02,
     3  0.1369994796354988D-01,0.1745537809875104D-01,
     4  0.2100399459023692D-01,0.2290877323724500D-01,
     5  0.2419183293233439D-01,0.2537390823544299D-01,
     6  0.2586326278013549D-01,0.2537390823544212D-01,
     7  0.2419183293233326D-01,0.2290877323724479D-01,
     8  0.2100399459023527D-01,0.1745537809874851D-01,
     9  0.1369994796355013D-01,0.9534654511785908D-02,
     *  0.5630991961860129D-02,0.1981669814506773D-02,
     1  0.3202372052766569D-02,0.8085787412743129D-02,
     2  0.1369994796355007D-01,0.1920220699859326D-01,
     3  0.2430742486685139D-01,0.2857915647737479D-01,
     4  0.3091976823578473D-01,0.3274602421745745D-01,
     5  0.3383753574696337D-01,0.3383753574696216D-01,
     6  0.3274602421745495D-01,0.3091976823578442D-01,
     7  0.2857915647737567D-01,0.2430742486685251D-01,
     8  0.1920220699859343D-01,0.1369994796354979D-01,
     9  0.8085787412742270D-02,0.3202372052766090D-02,
     *  0.4058173986634832D-02,0.1028616320645119D-01,
     1  0.1745537809874853D-01,0.2430742486685273D-01,
     2  0.3086443400800901D-01,0.3534152622451153D-01,
     3  0.3803306405288837D-01,0.4022748523361081D-01,
     4  0.4106605533804509D-01,0.4022748523360792D-01,
     5  0.3803306405288473D-01,0.3534152622450910D-01,
     6  0.3086443400800886D-01,0.2430742486685184D-01,
     7  0.1745537809875134D-01,0.1028616320645233D-01,
     8  0.4058173986635281D-02,0.5087747133030545D-02,
     9  0.1287520315340715D-01,0.2100399459023553D-01,
     *  0.2857915647737573D-01,0.3534152622450886D-01,
     1  0.3975288936073518D-01,0.4384400301738123D-01,
     2  0.4669645206838966D-01,0.4669645206838936D-01,
     3  0.4384400301738093D-01,0.3975288936073536D-01,
     4  0.3534152622451101D-01,0.2857915647737474D-01,
     5  0.2100399459023720D-01,0.1287520315340846D-01,
     6  0.5087747133031369D-02,0.6022218667400172D-02,
     7  0.1465709050187035D-01,0.2290877323724450D-01,
     8  0.3091976823578387D-01,0.3803306405288433D-01,
     9  0.4384400301738064D-01,0.4919209090625008D-01,
     *  0.5113735821968909D-01,0.4919209090625013D-01,
     1  0.4384400301738154D-01,0.3803306405288818D-01,
     2  0.3091976823578434D-01,0.2290877323724476D-01,
     3  0.1465709050187032D-01,0.6022218667400506D-02,
     4  0.6609045283599354D-02,0.1556608416800246D-01,
     5  0.2419183293233287D-01,0.3274602421745473D-01,
     6  0.4022748523360788D-01,0.4669645206838913D-01,
     7  0.5113735821968895D-01,0.5113735821968897D-01,
     8  0.4669645206838955D-01,0.4022748523361072D-01,
     9  0.3274602421745710D-01,0.2419183293233380D-01,
     *  0.1556608416800194D-01,0.6609045283599449D-02,
     1  0.6956974143949367D-02,0.1623974204539017D-01,
     2  0.2537390823544211D-01,0.3383753574696220D-01,
     3  0.4106605533804512D-01,0.4669645206838935D-01,
     4  0.4919209090624984D-01,0.4669645206838900D-01,
     5  0.4106605533804497D-01,0.3383753574696317D-01,
     6  0.2537390823544262D-01,0.1623974204538941D-01,
     7  0.6956974143949386D-02,0.7214151642671377D-02,
     8  0.1672692718714456D-01,0.2586326278013570D-01,
     9  0.3383753574696340D-01,0.4022748523361084D-01,
     *  0.4384400301738083D-01,0.4384400301738022D-01,
     1  0.4022748523360785D-01,0.3383753574696221D-01,
     2  0.2586326278013565D-01,0.1672692718714420D-01,
     3  0.7214151642671281D-02,0.7323832578681105D-02,
     4  0.1672692718714416D-01,0.2537390823544311D-01,
     5  0.3274602421745727D-01,0.3803306405288828D-01,
     6  0.3975288936073509D-01,0.3803306405288471D-01,
     7  0.3274602421745510D-01,0.2537390823544253D-01,
     8  0.1672692718714475D-01,0.7323832578681082D-02,
     9  0.7214151642671367D-02,0.1623974204538954D-01,
     *  0.2419183293233427D-01,0.3091976823578435D-01,
     1  0.3534152622451169D-01,0.3534152622450962D-01,
     2  0.3091976823578446D-01,0.2419183293233339D-01,
     3  0.1623974204539023D-01,0.7214151642671357D-02,
     4  0.6956974143949503D-02,0.1556608416800204D-01,
     5  0.2290877323724489D-01,0.2857915647737482D-01,
     6  0.3086443400800938D-01,0.2857915647737582D-01,
     7  0.2290877323724462D-01,0.1556608416800229D-01,
     8  0.6956974143949314D-02,0.6609045283599480D-02,
     9  0.1465709050187027D-01,0.2100399459023697D-01,
     *  0.2430742486685137D-01,0.2430742486685221D-01,
     1  0.2100399459023515D-01,0.1465709050187019D-01,
     2  0.6609045283599350D-02,0.6022218667400389D-02,
     3  0.1287520315340826D-01,0.1745537809875079D-01,
     4  0.1920220699859300D-01,0.1745537809874826D-01,
     5  0.1287520315340717D-01,0.6022218667400250D-02,
     6  0.5087747133031184D-02,0.1028616320645221D-01,
     7  0.1369994796354976D-01,0.1369994796355045D-01,
     8  0.1028616320645155D-01,0.5087747133030655D-02,
     9  0.4058173986635252D-02,0.8085787412742651D-02,
     *  0.9534654511786123D-02,0.8085787412743408D-02,
     1  0.4058173986634886D-02,0.3202372052766146D-02,
     2  0.5630991961860152D-02,0.5630991961858260D-02,
     3  0.3202372052766471D-02,0.1981669814506699D-02,
     4  0.3057113443011740D-02,0.1981669814505677D-02,
     5  0.7702153068307515D-03,0.7702153068313153D-03,
     6  0.4038074242045246D-03/


c
        npols=0
c        
        if( norder .eq. 0 ) then
        npols=1
        call ortho2arrmove(xs0,xsout,npols)
        call ortho2arrmove(ys0,ysout,npols)
        call ortho2arrmove(ws0,wsout,npols)
        endif
c
        if( norder .eq. 1 ) then
        npols=3
        call ortho2arrmove(xs1,xsout,npols)
        call ortho2arrmove(ys1,ysout,npols)
        call ortho2arrmove(ws1,wsout,npols)
        endif
c
        if( norder .eq. 2 ) then
        npols=6
        call ortho2arrmove(xs2,xsout,npols)
        call ortho2arrmove(ys2,ysout,npols)
        call ortho2arrmove(ws2,wsout,npols)
        endif
c
        if( norder .eq. 3 ) then
        npols=10
        call ortho2arrmove(xs3,xsout,npols)
        call ortho2arrmove(ys3,ysout,npols)
        call ortho2arrmove(ws3,wsout,npols)
        endif
c
        if( norder .eq. 4 ) then
        npols=15
        call ortho2arrmove(xs4,xsout,npols)
        call ortho2arrmove(ys4,ysout,npols)
        call ortho2arrmove(ws4,wsout,npols)
        endif
c
        if( norder .eq. 5 ) then
        npols=21
        call ortho2arrmove(xs5,xsout,npols)
        call ortho2arrmove(ys5,ysout,npols)
        call ortho2arrmove(ws5,wsout,npols)
        endif
c
        if( norder .eq. 6 ) then
        npols=28
        call ortho2arrmove(xs6,xsout,npols)
        call ortho2arrmove(ys6,ysout,npols)
        call ortho2arrmove(ws6,wsout,npols)
        endif
c
        if( norder .eq. 7 ) then
        npols=36
        call ortho2arrmove(xs7,xsout,npols)
        call ortho2arrmove(ys7,ysout,npols)
        call ortho2arrmove(ws7,wsout,npols)
        endif
c
        if( norder .eq. 8 ) then
        npols=45
        call ortho2arrmove(xs8,xsout,npols)
        call ortho2arrmove(ys8,ysout,npols)
        call ortho2arrmove(ws8,wsout,npols)
        endif
c
        if( norder .eq. 9 ) then
        npols=55
        call ortho2arrmove(xs9,xsout,npols)
        call ortho2arrmove(ys9,ysout,npols)
        call ortho2arrmove(ws9,wsout,npols)
        endif
c
        if( norder .eq. 10 ) then
        npols=66
        call ortho2arrmove(xs10,xsout,npols)
        call ortho2arrmove(ys10,ysout,npols)
        call ortho2arrmove(ws10,wsout,npols)
        endif
c
        if( norder .eq. 11 ) then
        npols=78
        call ortho2arrmove(xs11,xsout,npols)
        call ortho2arrmove(ys11,ysout,npols)
        call ortho2arrmove(ws11,wsout,npols)
        endif
c
        if( norder .eq. 12 ) then
        npols=91
        call ortho2arrmove(xs12,xsout,npols)
        call ortho2arrmove(ys12,ysout,npols)
        call ortho2arrmove(ws12,wsout,npols)
        endif
c
        if( norder .eq. 13 ) then
        npols=105
        call ortho2arrmove(xs13,xsout,npols)
        call ortho2arrmove(ys13,ysout,npols)
        call ortho2arrmove(ws13,wsout,npols)
        endif
c
        if( norder .eq. 14 ) then
        npols=120
        call ortho2arrmove(xs14,xsout,npols)
        call ortho2arrmove(ys14,ysout,npols)
        call ortho2arrmove(ws14,wsout,npols)
        endif
c
        if( norder .eq. 15 ) then
        npols=136
        call ortho2arrmove(xs15,xsout,npols)
        call ortho2arrmove(ys15,ysout,npols)
        call ortho2arrmove(ws15,wsout,npols)
        endif
c
        if( norder .eq. 16 ) then
        npols=153
        call ortho2arrmove(xs16,xsout,npols)
        call ortho2arrmove(ys16,ysout,npols)
        call ortho2arrmove(ws16,wsout,npols)
        endif
c
        if( norder .eq. 17 ) then
        npols=171
        call ortho2arrmove(xs17,xsout,npols)
        call ortho2arrmove(ys17,ysout,npols)
        call ortho2arrmove(ws17,wsout,npols)
        endif
c
        if( norder .eq. 18 ) then
        npols=190
        call ortho2arrmove(xs18,xsout,npols)
        call ortho2arrmove(ys18,ysout,npols)
        call ortho2arrmove(ws18,wsout,npols)
        endif
c
        if( norder .eq. 19 ) then
        npols=210
        call ortho2arrmove(xs19,xsout,npols)
        call ortho2arrmove(ys19,ysout,npols)
        call ortho2arrmove(ws19,wsout,npols)
        endif
c
        if( norder .eq. 20 ) then
        npols=231
        call ortho2arrmove(xs20,xsout,npols)
        call ortho2arrmove(ys20,ysout,npols)
        call ortho2arrmove(ws20,wsout,npols)
        endif
c
c
c       on the standard triangle, the sum of the weights should be
c       sqrt(3.0d0)  
c       
        d=0
        do 1200 i=1,npols
        d=d+wsout(i)
 1200 continue
c
ccc        call prin2('in ortho2smexps, sum of weights=*',d,1)
c
        do 1400 i=1,npols
        wsout(i)=wsout(i)/d
        wsout(i)=wsout(i)*sqrt(3.0d0)
 1400 continue
c
c       get the interpolation matrices
c
        call ortho2intpmatr(norder,xsout,ysout,npols,umatr,vmatr)
c
        return
        end
c
c
c
c
c
        subroutine ortho2sfexps(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
        implicit real *8 (a-h,o-z)
        dimension xs0(1),ys0(1),ws0(1)
        dimension xs1(3),ys1(3),ws1(3)
        dimension xs2(6),ys2(6),ws2(6)
        dimension xs3(10),ys3(10),ws3(10)
        dimension xs4(15),ys4(15),ws4(15)
        dimension xs5(21),ys5(21),ws5(21)
        dimension xs6(28),ys6(28),ws6(28)
        dimension xs7(36),ys7(36),ws7(36)
        dimension xs8(45),ys8(45),ws8(45)
        dimension xs9(55),ys9(55),ws9(55)
        dimension xs10(66),ys10(66),ws10(66)
        dimension xs11(78),ys11(78),ws11(78)
        dimension xs12(91),ys12(91),ws12(91)
        dimension xs13(105),ys13(105),ws13(105)
        dimension xs14(120),ys14(120),ws14(120)
        dimension xs15(136),ys15(136),ws15(136)
        dimension xs16(153),ys16(153),ws16(153)
        dimension xs17(171),ys17(171),ws17(171)
        dimension xs18(190),ys18(190),ws18(190)
        dimension xs19(210),ys19(210),ws19(210)
        dimension xs20(231),ys20(231),ws20(231)
        dimension xsout(1),ysout(1),wsout(1),umatr(1),vmatr(1)
c
c       This subroutine constructs (or rather retrieves) the
c       interpolation nodes for the polynomials (i.e. smooth functions)
c       on the standard triangle with the vertices
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))            (1)
c
c       and the corresponding quadrature weights. It also constructs the
c       matrix vmatr converting the coefficients of the polynomial
c       expansion to its values at the interpolation nodes, and its
c       inverse umatr, converting the values of a function at the
c       interpolation nodes into the coefficients of the polynomial
c       expansion.
c       
c       The constructed nodes are as far away from the boundary as
c       reasonably possible. The quadrature is of low order and will
c       integrate only the polynomials itself but not their pairwise
c       products (user beware).
c
c       The tables are valid up to order 20.
c       
c
c       NOTE #1: the nodes are fully symmetric for all orders
c
c       NOTE #2: the nodes are chebychev-like - they integrate only the 
c       polynomials up to order of interpolation
c       
c       NOTE #3: the weights are positive only for orders 0,1,2,3,4,5,6,7,8
c
c       NOTE #4: the weights are accurate to 30 digits
c       
c
c interp    0     1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------------
c quadr     1     1     2     3     4     5     6     7     8     9    10
c  -----------------------------------------------------------------------
c nodes     1     3     6    10    15    21    28    36    45    55    66
c  -----------------------------------------------------------------------
c cond #   1.0   1.1   1.4   2.1   2.6   3.6   5.2   7.2  10.3  16.0  24.3  
c
c
c interp   11    12    13    14    15    16    17    18    19    20  
c  -----------------------------------------------------------------------
c quadr    11    12    13    14    15    16    17    18    19    20  
c  -----------------------------------------------------------------------
c nodes    78    91   105   120   136   153   171   190   210   231
c  -----------------------------------------------------------------------
c cond #  37.8  60.5   90   158   256   422   699  1155  1925  3234
c
c       
c
c         Input parameters:
c
c    itype - the type of the calculation to be performed. currently
c          unused
c    norder - the order of the expansion
c
c
c         Output parameters:
c
c    npols - the number of the polynomials, i.e. the terms in the
c          expansion
c    xsout - the x-coordinates of the interpolation nodes (npols of them)
c    ysout - the y-coordinates of the interpolation nodes (npols of them)
c    umatr - the npols*npols matrix, converting the values of the polynomial
c          at the interpolation nodes into the coefficients of its expansion
c    vmatr - the npols*npols matrix, converting the coefficients of 
c          the expansion into its values at the interpolation nodes.
c    wsout - the corresponding quadrature weigths (npols of them)
c
c
c
c    ... interpolation of order  0 , quadratures of order  1
c                   total number of elements is    1
      data xs0/
     1    0.00000000000000000000000000000000D+00/
      data ys0/
     1    0.00000000000000000000000000000000D+00/
      data ws0/
     1    0.45590141139095552839871265039273D+01/

c    ... interpolation of order  1 , quadratures of order  1
c                   total number of elements is    3
      data xs1/
     1    0.46415888336127788924100763509194D+00,
     2    0.00000000000000000000000000000000D+00,
     3   -0.46415888336127788924100763509194D+00/
      data ys1/
     1   -0.26798225625538989664814310113757D+00,
     2    0.53596451251077979329628620227513D+00,
     3   -0.26798225625538989664814310113757D+00/
      data ws1/
     1    0.15196713713031850946623755013091D+01,
     2    0.15196713713031850946623755013091D+01,
     3    0.15196713713031850946623755013091D+01/

c    ... interpolation of order  2 , quadratures of order  2
c                   total number of elements is    6
      data xs2/
     1    0.00000000000000000000000000000000D+00,
     2   -0.67832018593257859350609427420699D+00,
     3    0.00000000000000000000000000000000D+00,
     4   -0.31034913895002041968195023999520D+00,
     5    0.67832018593257859350609427420699D+00,
     6    0.31034913895002041968195023999520D+00/
      data ys2/
     1    0.78325668388986250132767669218768D+00,
     2   -0.39162834194493125066383834609384D+00,
     3   -0.35836031783112571919404106205974D+00,
     4    0.17918015891556285959702053102987D+00,
     5   -0.39162834194493125066383834609384D+00,
     6    0.17918015891556285959702053102987D+00/
      data ws2/
     1    0.64196591163172639778448830312248D+00,
     2    0.64196591163172639778448830312249D+00,
     3    0.87770545967145869687788719818660D+00,
     4    0.87770545967145869687788719818661D+00,
     5    0.64196591163172639778448830312248D+00,
     6    0.87770545967145869687788719818661D+00/

c    ... interpolation of order  3 , quadratures of order  3
c                   total number of elements is   10
      data xs3/
     1    0.00000000000000000000000000000000D+00,
     2    0.78788216465527050157292367904690D+00,
     3    0.00000000000000000000000000000000D+00,
     4    0.30244045274895719698094298757284D+00,
     5   -0.78788216465527050157292367904690D+00,
     6    0.21311173024631953814873643150884D+00,
     7    0.51555218299527673512967941908167D+00,
     8   -0.21311173024631953814873643150884D+00,
     9   -0.30244045274895719698094298757284D+00,
     *   -0.51555218299527673512967941908167D+00/
      data ys3/
     1    0.00000000000000000000000000000000D+00,
     2   -0.45488397985342547416677111801510D+00,
     3    0.90976795970685094833354223603020D+00,
     4   -0.42069430645880172198535665595501D+00,
     5   -0.45488397985342547416677111801510D+00,
     6    0.47226826844206495481884960515937D+00,
     7   -0.51573961983263232833492949204358D-01,
     8    0.47226826844206495481884960515937D+00,
     9   -0.42069430645880172198535665595501D+00,
     *   -0.51573961983263232833492949204358D-01/
      data ws3/
     1    0.46025308671472636701469243761513D+00,
     2    0.24995530577052860345843403939641D+00,
     3    0.24995530577052860345843403939641D+00,
     4    0.55814918498054051776618865802049D+00,
     5    0.24995530577052860345843403939641D+00,
     6    0.55814918498054051776618865802049D+00,
     7    0.55814918498054051776618865802048D+00,
     8    0.55814918498054051776618865802049D+00,
     9    0.55814918498054051776618865802049D+00,
     *    0.55814918498054051776618865802049D+00/

c    ... interpolation of order  4 , quadratures of order  4
c                   total number of elements is   15
      data xs4/
     1    0.00000000000000000000000000000000D+00,
     2   -0.23972386206643138870022060309036D+00,
     3    0.23972386206643138870022060309036D+00,
     4   -0.38899223152341886863742013327792D+00,
     5    0.38899223152341886863742013327792D+00,
     6    0.00000000000000000000000000000000D+00,
     7   -0.15329324466609596024679230250707D+00,
     8   -0.64639706055370659632540592170819D+00,
     9    0.15329324466609596024679230250707D+00,
     *   -0.49310381588761063607861361920111D+00,
     1    0.64639706055370659632540592170819D+00,
     2    0.49310381588761063607861361920111D+00,
     3    0.00000000000000000000000000000000D+00,
     4   -0.85029803182531372977585557799028D+00,
     5    0.85029803182531372977585557799028D+00/
      data ys4/
     1    0.27680927259046175750309741683553D+00,
     2   -0.13840463629523087875154870841777D+00,
     3   -0.13840463629523087875154870841777D+00,
     4    0.22458476958271911289823828457629D+00,
     5    0.22458476958271911289823828457629D+00,
     6   -0.44916953916543822579647656915258D+00,
     7    0.65789113775520899169682606160723D+00,
     8   -0.19618972476822199603512010753417D+00,
     9    0.65789113775520899169682606160723D+00,
     *   -0.46170141298698699566170595407306D+00,
     1   -0.19618972476822199603512010753417D+00,
     2   -0.46170141298698699566170595407306D+00,
     3    0.98183959513150771448196632834670D+00,
     4   -0.49091979756575385724098316417335D+00,
     5   -0.49091979756575385724098316417335D+00/
      data ws4/
     1    0.38536461720928538094483065736917D+00,
     2    0.38536461720928538094483065736917D+00,
     3    0.38536461720928538094483065736917D+00,
     4    0.46041105370763293999333328547198D+00,
     5    0.46041105370763293999333328547198D+00,
     6    0.46041105370763293999333328547198D+00,
     7    0.26148049688917298463576027725449D+00,
     8    0.26148049688917298463576027725449D+00,
     9    0.26148049688917298463576027725449D+00,
     *    0.26148049688917298463576027725449D+00,
     1    0.26148049688917298463576027725449D+00,
     2    0.26148049688917298463576027725449D+00,
     3    0.15093470660792080445269100395896D+00,
     4    0.15093470660792080445269100395896D+00,
     5    0.15093470660792080445269100395896D+00/

c    ... interpolation of order  5 , quadratures of order  5
c                   total number of elements is   21
      data xs5/
     1    0.41193815627014371079326648710691D+00,
     2   -0.41193815627014371079326648710691D+00,
     3    0.00000000000000000000000000000000D+00,
     4    0.00000000000000000000000000000000D+00,
     5    0.18688344341943277183810695904776D+00,
     6   -0.18688344341943277183810695904776D+00,
     7   -0.22087079446412901939648332653987D+00,
     8    0.22087079446412901939648332653987D+00,
     9   -0.52022362368298212987744816558859D+00,
     *    0.52022362368298212987744816558859D+00,
     1   -0.29935282921885311048096483904872D+00,
     2    0.29935282921885311048096483904872D+00,
     3    0.61744831068503331198337271047326D+00,
     4   -0.61744831068503331198337271047326D+00,
     5    0.73236948567739838452344328062193D+00,
     6   -0.73236948567739838452344328062193D+00,
     7    0.11492117499236507254007057014867D+00,
     8   -0.11492117499236507254007057014867D+00,
     9    0.88894196789837802998851710379702D+00,
     *   -0.88894196789837802998851710379702D+00,
     1    0.00000000000000000000000000000000D+00/
      data ys5/
     1   -0.23783260541204559590836581117600D+00,
     2   -0.23783260541204559590836581117600D+00,
     3   -0.21579441273058741296131773275289D+00,
     4    0.47566521082409119181673162235199D+00,
     5    0.10789720636529370648065886637644D+00,
     6    0.10789720636529370648065886637644D+00,
     7   -0.47318268570435321806981628061863D+00,
     8   -0.47318268570435321806981628061863D+00,
     9    0.45311623892189518849004043640292D-01,
     *    0.45311623892189518849004043640293D-01,
     1    0.42787106181216369922081223697834D+00,
     2    0.42787106181216369922081223697834D+00,
     3   -0.48918349101954379139295532568329D+00,
     4   -0.48918349101954379139295532568329D+00,
     5   -0.29013417706725360166266186337471D+00,
     6   -0.29013417706725360166266186337471D+00,
     7    0.77931766808679739305561718905801D+00,
     8    0.77931766808679739305561718905800D+00,
     9   -0.51323088446008422054455754397817D+00,
     *   -0.51323088446008422054455754397817D+00,
     1    0.10264617689201684410891150879563D+01/
      data ws5/
     1    0.12638977104632570791478878677807D+00,
     2    0.12638977104632570791478878677807D+00,
     3    0.39575825924905674143686932248044D+00,
     4    0.12638977104632570791478878677807D+00,
     5    0.39575825924905674143686932248044D+00,
     6    0.39575825924905674143686932248044D+00,
     7    0.26817695580187041441140059477997D+00,
     8    0.26817695580187041441140059477997D+00,
     9    0.26817695580187041441140059477997D+00,
     *    0.26817695580187041441140059477997D+00,
     1    0.26817695580187041441140059477997D+00,
     2    0.26817695580187041441140059477997D+00,
     3    0.19929766319442293259086293623194D+00,
     4    0.19929766319442293259086293623194D+00,
     5    0.19929766319442293259086293623194D+00,
     6    0.19929766319442293259086293623194D+00,
     7    0.19929766319442293259086293623194D+00,
     8    0.19929766319442293259086293623194D+00,
     9    0.62574103015215951306190330026757D-01,
     *    0.62574103015215951306190330026760D-01,
     1    0.62574103015215951306190330026757D-01/

c    ... interpolation of order  6 , quadratures of order  6
c                   total number of elements is   28
      data xs6/
     1    0.00000000000000000000000000000000D+00,
     2    0.14687095265546441293319920910959D+00,
     3   -0.18997843604320623243394440306687D+00,
     4   -0.14687095265546441293319920910959D+00,
     5   -0.33684938869867064536714361217645D+00,
     6    0.33684938869867064536714361217645D+00,
     7    0.18997843604320623243394440306686D+00,
     8   -0.42113790169293314466222148402808D+00,
     9    0.42113790169293314466222148402808D+00,
     *    0.00000000000000000000000000000000D+00,
     1    0.00000000000000000000000000000000D+00,
     2    0.23589680919441244787695651408205D+00,
     3   -0.23589680919441244787695651408205D+00,
     4   -0.53512505183737187699766690948759D+00,
     5   -0.61661030181743567476511247296515D+00,
     6   -0.38071349262302322688815595888310D+00,
     7    0.61661030181743567476511247296515D+00,
     8    0.53512505183737187699766690948759D+00,
     9    0.38071349262302322688815595888310D+00,
     *    0.89111545368878451512522581690287D-01,
     1   -0.89111545368878451512522581690287D-01,
     2    0.79112821373707380071602697557590D+00,
     3   -0.79112821373707380071602697557590D+00,
     4    0.70201666836819534920350439388561D+00,
     5   -0.70201666836819534920350439388561D+00,
     6    0.00000000000000000000000000000000D+00,
     7   -0.91443477721301411271065597460659D+00,
     8    0.91443477721301411271065597460660D+00/
      data ys6/
     1    0.00000000000000000000000000000000D+00,
     2    0.30416418643130759999470854434220D+00,
     3   -0.27927606929330753970993788755555D+00,
     4    0.30416418643130759999470854434220D+00,
     5   -0.24888117138000060284770656786648D-01,
     6   -0.24888117138000060284770656786649D-01,
     7   -0.27927606929330753970993788755555D+00,
     8    0.24314408090836910304205067796880D+00,
     9    0.24314408090836910304205067796880D+00,
     *   -0.48628816181673820608410135593759D+00,
     1    0.61790918545683818900059483210380D+00,
     2    0.57580516118941793833689623929834D+00,
     3    0.57580516118941793833689623929834D+00,
     4   -0.30895459272841909450029741605190D+00,
     5   -0.83609951160657249867245249661185D-01,
     6   -0.49219521002876068846965098963716D+00,
     7   -0.83609951160657249867245249661185D-01,
     8   -0.30895459272841909450029741605190D+00,
     9   -0.49219521002876068846965098963716D+00,
     *    0.86206759962258916981557725132830D+00,
     1    0.86206759962258916981557725132830D+00,
     2   -0.35386093775135630021845316228634D+00,
     3   -0.35386093775135630021845316228635D+00,
     4   -0.50820666187123286959712408904195D+00,
     5   -0.50820666187123286959712408904196D+00,
     6    0.10558983295605783239941289792754D+01,
     7   -0.52794916478028916199706448963770D+00,
     8   -0.52794916478028916199706448963770D+00/
      data ws6/
     1    0.52290087589095112116098763963412D+00,
     2    0.15938565984376537102515341667300D+00,
     3    0.15938565984376537102515341667299D+00,
     4    0.15938565984376537102515341667299D+00,
     5    0.15938565984376537102515341667300D+00,
     6    0.15938565984376537102515341667299D+00,
     7    0.15938565984376537102515341667301D+00,
     8    0.18306860293501539303141502279525D+00,
     9    0.18306860293501539303141502279526D+00,
     *    0.18306860293501539303141502279526D+00,
     1    0.17335582343300785579300470283073D+00,
     2    0.22398640455257016309892669626206D+00,
     3    0.22398640455257016309892669626207D+00,
     4    0.17335582343300785579300470283073D+00,
     5    0.22398640455257016309892669626206D+00,
     6    0.22398640455257016309892669626207D+00,
     7    0.22398640455257016309892669626206D+00,
     8    0.17335582343300785579300470283073D+00,
     9    0.22398640455257016309892669626205D+00,
     *    0.83123648235274701911512893045900D-01,
     1    0.83123648235274701911512893045894D-01,
     2    0.83123648235274701911512893045900D-01,
     3    0.83123648235274701911512893045902D-01,
     4    0.83123648235274701911512893045903D-01,
     5    0.83123648235274701911512893045897D-01,
     6    0.55955227708291000046440550509816D-01,
     7    0.55955227708291000046440550509814D-01,
     8    0.55955227708291000046440550509812D-01/

c    ... interpolation of order  7 , quadratures of order  7
c                   total number of elements is   36
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c    ... interpolation of order  8 , quadratures of order  8
c                   total number of elements is   45
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c    ... interpolation of order  9 , quadratures of order  9
c                   total number of elements is   55
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      data ws9/
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c    ... interpolation of order  10 , quadratures of order  10
c                   total number of elements is   66
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      data ys10/
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c    ... interpolation of order  11 , quadratures of order  11
c                   total number of elements is   78
      data xs11/
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c    ... interpolation of order  12 , quadratures of order  12
c                   total number of elements is   91
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c    ... interpolation of order  13, quadratures of order  13
c                   total number of elements is  105
      data xs13/
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c    ... interpolation of order  14 , quadratures of order  14
c                   total number of elements is  120
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c    ... interpolation of order  15 , quadratures of order  15
c                   total number of elements is  136
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c    ... interpolation of order  16 , quadratures of order  16
c                   total number of elements is  153
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c    ... interpolation of order  17 , quadratures of order  17
c                   total number of elements is  171
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c    ... interpolation of order  18 , quadratures of order  18
c                   total number of elements is  190
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c    ... interpolation of order  19 , quadratures of order  19
c                   total number of elements is  210
      data xs19/
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c    ... interpolation of order  20 , quadratures of order  20
c                   total number of elements is  231
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     7    0.32324383995584489202992488996265D+01,
     8    0.18001313334536905342938395875561D+01,
     9    0.32324383995584489202992488996254D+01,
     *    0.57676360341285471229237289002658D+00,
     1   -0.53387020140518541170129523195534D+00,
     2    0.57676360341285471229237289002549D+00,
     3    0.96814063161988171933035120736545D+00,
     4    0.96814063161988171933035120736582D+00,
     5   -0.53387020140518541170129523195589D+00,
     6    0.96814063161988171933035120736605D+00,
     7    0.96814063161988171933035120736638D+00,
     8    0.32668938338377438142475728466391D-01,
     9    0.32668938338377438142475728467011D-01,
     *   -0.18085622981308699557207674498082D+01,
     1   -0.18085622981308699557207674498081D+01,
     2   -0.81157599199666935486629252546406D+00,
     3   -0.29615899669439584289175758012984D+01,
     4   -0.29615899669439584289175758013011D+01,
     5   -0.18085622981308699557207674498080D+01,
     6   -0.19803133802594683465081614893713D+00,
     7   -0.81157599199666935486629252546430D+00,
     8   -0.81157599199666935486629252546521D+00,
     9   -0.29615899669439584289175758013000D+01,
     *   -0.19803133802594683465081614893787D+00,
     1   -0.29615899669439584289175758012973D+01,
     2   -0.18085622981308699557207674498067D+01,
     3    0.32668938338377438142475728466337D-01,
     4    0.23995902936885286233939377051913D-01,
     5    0.35490234811487203814788058245380D-01,
     6   -0.81157599199666935486629252546442D+00,
     7    0.35490234811487203814788058245277D-01,
     8    0.32668938338377438142475728467361D-01,
     9   -0.19803133802594683465081614893734D+00,
     *    0.32668938338377438142475728466991D-01,
     1    0.13990049480073517258091015021629D+01,
     2    0.32668938338377438142475728466460D-01,
     3    0.30794620575244883480377140707374D+00,
     4   -0.19803133802594683465081614893783D+00,
     5    0.22274866647314332559297910369075D+01,
     6   -0.18085622981308699557207674498058D+01,
     7   -0.81157599199666935486629252546542D+00,
     8   -0.29615899669439584289175758013024D+01,
     9   -0.29615899669439584289175758012970D+01,
     *   -0.18085622981308699557207674498085D+01,
     1   -0.19803133802594683465081614893834D+00,
     2   -0.81157599199666935486629252546479D+00,
     3    0.23995902936885286233939377051250D-01,
     4    0.40667798716642865205294583847549D+01,
     5    0.22274866647314332559297910369073D+01,
     6    0.13990049480073517258091015021643D+01,
     7    0.35490234811487203814788058245986D-01,
     8    0.36723757368068773418007821464043D-01,
     9    0.30794620575244883480377140707403D+00,
     *    0.35490234811487203814788058245950D-01,
     1   -0.19803133802594683465081614893735D+00,
     2    0.36723757368068773418007821463516D-01,
     3    0.13990049480073517258091015021629D+01,
     4    0.30794620575244883480377140707435D+00,
     5    0.22274866647314332559297910369094D+01,
     6    0.36723757368068773418007821464270D-01,
     7    0.23995902936885286233939377051809D-01,
     8    0.40667798716642865205294583847494D+01,
     9    0.22274866647314332559297910369067D+01,
     *    0.13990049480073517258091015021632D+01,
     1    0.35490234811487203814788058245356D-01,
     2    0.30794620575244883480377140707422D+00,
     3    0.35490234811487203814788058245509D-01,
     4    0.36723757368068773418007821464209D-01,
     5    0.13990049480073517258091015021644D+01,
     6    0.30794620575244883480377140707508D+00,
     7    0.22274866647314332559297910369034D+01,
     8    0.40667798716642865205294583847576D+01,
     9    0.22274866647314332559297910369060D+01,
     *    0.13990049480073517258091015021636D+01,
     1    0.30794620575244883480377140707409D+00,
     2    0.36723757368068773418007821463563D-01,
     3    0.36723757368068773418007821463913D-01,
     4   -0.52075770719018062240620860058457D+00,
     5   -0.16195284977591741045599351933753D+01,
     6   -0.36986337119731641819373016346688D-02,
     7   -0.16195284977591741045599351933758D+01,
     8   -0.34061833855785287844937065522128D+01,
     9   -0.52075770719018062240620860058510D+00,
     *   -0.34061833855785287844937065522133D+01,
     1   -0.36986337119731641819373016341988D-02,
     2   -0.52075770719018062240620860058542D+00,
     3   -0.52075770719018062240620860058606D+00,
     4   -0.36986337119731641819373016349891D-02,
     5   -0.16195284977591741045599351933735D+01,
     6   -0.34061833855785287844937065522138D+01,
     7   -0.16195284977591741045599351933741D+01,
     8   -0.34061833855785287844937065522095D+01,
     9   -0.52075770719018062240620860058504D+00,
     *   -0.36986337119731641819373016349572D-02,
     1   -0.16195284977591741045599351933753D+01,
     2   -0.36986337119731641819373016343100D-02,
     3   -0.16195284977591741045599351933763D+01,
     4   -0.52075770719018062240620860058507D+00,
     5   -0.34061833855785287844937065522101D+01,
     6   -0.34061833855785287844937065522127D+01,
     7   -0.36986337119731641819373016345319D-02,
     8    0.87489086312608674368058719765890D-01,
     9    0.74508897763741391573473445147461D+00,
     *    0.23563752359135064440782448718579D+01,
     1    0.74508897763741391573473445147492D+00,
     2    0.23563752359135064440782448718585D+01,
     3    0.87489086312608674368058719765523D-01,
     4    0.37378850970820946871482684300363D+01,
     5    0.87489086312608674368058719766269D-01,
     6    0.74508897763741391573473445147489D+00,
     7    0.23563752359135064440782448718568D+01,
     8    0.74508897763741391573473445147464D+00,
     9    0.23563752359135064440782448718554D+01,
     *    0.87489086312608674368058719766258D-01,
     1    0.37378850970820946871482684300353D+01,
     2    0.87489086312608674368058719765634D-01,
     3    0.74508897763741391573473445147585D+00,
     4    0.23563752359135064440782448718571D+01,
     5    0.74508897763741391573473445147573D+00,
     6    0.23563752359135064440782448718572D+01,
     7    0.87489086312608674368058719765766D-01,
     8    0.37378850970820946871482684300360D+01,
     9   -0.10257522547168438174391638272415D+00,
     *   -0.10523247482990051396003665515341D+01,
     1   -0.10257522547168438174391638272373D+00,
     2   -0.10523247482990051396003665515343D+01,
     3   -0.28962999275530534265650564518549D+01,
     4   -0.28962999275530534265650564518584D+01,
     5   -0.10257522547168438174391638272456D+00,
     6   -0.10257522547168438174391638272401D+00,
     7   -0.10523247482990051396003665515336D+01,
     8   -0.10523247482990051396003665515350D+01,
     9   -0.10257522547168438174391638272453D+00,
     *   -0.10257522547168438174391638272407D+00,
     1   -0.10523247482990051396003665515338D+01,
     2   -0.10523247482990051396003665515341D+01,
     3   -0.28962999275530534265650564518581D+01,
     4   -0.28962999275530534265650564518547D+01,
     5   -0.28962999275530534265650564518525D+01,
     6   -0.28962999275530534265650564518581D+01,
     7    0.21135699521591149324210438846983D+00,
     8    0.21135699521591149324210438846950D+00,
     9    0.14228592296672103692219573722396D+01,
     *    0.14228592296672103692219573722405D+01,
     1    0.28074681921931506826134459473844D+01,
     2    0.21135699521591149324210438846971D+00,
     3    0.14228592296672103692219573722416D+01,
     4    0.21135699521591149324210438846980D+00,
     5    0.28074681921931506826134459473816D+01,
     6    0.14228592296672103692219573722412D+01,
     7    0.21135699521591149324210438847033D+00,
     8    0.21135699521591149324210438847022D+00,
     9    0.14228592296672103692219573722391D+01,
     *    0.14228592296672103692219573722384D+01,
     1    0.28074681921931506826134459473834D+01,
     2   -0.29846664649762245169797012897360D+00,
     3   -0.29846664649762245169797012897336D+00,
     4   -0.16310839996220256306799438199049D+01,
     5   -0.16310839996220256306799438199061D+01,
     6   -0.29846664649762245169797012897363D+00,
     7   -0.29846664649762245169797012897372D+00,
     8   -0.16310839996220256306799438199058D+01,
     9   -0.16310839996220256306799438199052D+01,
     *   -0.29846664649762245169797012897382D+00,
     1   -0.29846664649762245169797012897374D+00,
     2   -0.16310839996220256306799438199041D+01,
     3   -0.16310839996220256306799438199042D+01,
     4    0.42703635857884771310000826174281D+00,
     5    0.42703635857884771310000826174258D+00,
     6    0.12244477220743937791163951755651D+01,
     7    0.42703635857884771310000826174294D+00,
     8    0.42703635857884771310000826174316D+00,
     9    0.12244477220743937791163951755650D+01,
     *    0.42703635857884771310000826174295D+00,
     1    0.42703635857884771310000826174286D+00,
     2    0.12244477220743937791163951755636D+01,
     3   -0.40343836282985897763993503570624D+00,
     4   -0.40343836282985897763993503570578D+00,
     5    0.16874927184774097687139833882198D+00,
     6   -0.40343836282985897763993503570610D+00,
     7   -0.40343836282985897763993503570651D+00,
     8   -0.40343836282985897763993503570578D+00,
     9   -0.40343836282985897763993503570606D+00,
     *    0.16874927184774097687139833882237D+00,
     1    0.16874927184774097687139833882237D+00/


c
        npols=0
c        
        if( norder .eq. 0 ) then
        npols=1
        call ortho2arrmove(xs0,xsout,npols)
        call ortho2arrmove(ys0,ysout,npols)
        call ortho2arrmove(ws0,wsout,npols)
        endif
c
        if( norder .eq. 1 ) then
        npols=3
        call ortho2arrmove(xs1,xsout,npols)
        call ortho2arrmove(ys1,ysout,npols)
        call ortho2arrmove(ws1,wsout,npols)
        endif
c
        if( norder .eq. 2 ) then
        npols=6
        call ortho2arrmove(xs2,xsout,npols)
        call ortho2arrmove(ys2,ysout,npols)
        call ortho2arrmove(ws2,wsout,npols)
        endif
c
        if( norder .eq. 3 ) then
        npols=10
        call ortho2arrmove(xs3,xsout,npols)
        call ortho2arrmove(ys3,ysout,npols)
        call ortho2arrmove(ws3,wsout,npols)
        endif
c
        if( norder .eq. 4 ) then
        npols=15
        call ortho2arrmove(xs4,xsout,npols)
        call ortho2arrmove(ys4,ysout,npols)
        call ortho2arrmove(ws4,wsout,npols)
        endif
c
        if( norder .eq. 5 ) then
        npols=21
        call ortho2arrmove(xs5,xsout,npols)
        call ortho2arrmove(ys5,ysout,npols)
        call ortho2arrmove(ws5,wsout,npols)
        endif
c
        if( norder .eq. 6 ) then
        npols=28
        call ortho2arrmove(xs6,xsout,npols)
        call ortho2arrmove(ys6,ysout,npols)
        call ortho2arrmove(ws6,wsout,npols)
        endif
c
        if( norder .eq. 7 ) then
        npols=36
        call ortho2arrmove(xs7,xsout,npols)
        call ortho2arrmove(ys7,ysout,npols)
        call ortho2arrmove(ws7,wsout,npols)
        endif
c
        if( norder .eq. 8 ) then
        npols=45
        call ortho2arrmove(xs8,xsout,npols)
        call ortho2arrmove(ys8,ysout,npols)
        call ortho2arrmove(ws8,wsout,npols)
        endif
c
        if( norder .eq. 9 ) then
        npols=55
        call ortho2arrmove(xs9,xsout,npols)
        call ortho2arrmove(ys9,ysout,npols)
        call ortho2arrmove(ws9,wsout,npols)
        endif
c
        if( norder .eq. 10 ) then
        npols=66
        call ortho2arrmove(xs10,xsout,npols)
        call ortho2arrmove(ys10,ysout,npols)
        call ortho2arrmove(ws10,wsout,npols)
        endif
c
        if( norder .eq. 11 ) then
        npols=78
        call ortho2arrmove(xs11,xsout,npols)
        call ortho2arrmove(ys11,ysout,npols)
        call ortho2arrmove(ws11,wsout,npols)
        endif
c
        if( norder .eq. 12 ) then
        npols=91
        call ortho2arrmove(xs12,xsout,npols)
        call ortho2arrmove(ys12,ysout,npols)
        call ortho2arrmove(ws12,wsout,npols)
        endif
c
        if( norder .eq. 13 ) then
        npols=105
        call ortho2arrmove(xs13,xsout,npols)
        call ortho2arrmove(ys13,ysout,npols)
        call ortho2arrmove(ws13,wsout,npols)
        endif
c
        if( norder .eq. 14 ) then
        npols=120
        call ortho2arrmove(xs14,xsout,npols)
        call ortho2arrmove(ys14,ysout,npols)
        call ortho2arrmove(ws14,wsout,npols)
        endif
c
        if( norder .eq. 15 ) then
        npols=136
        call ortho2arrmove(xs15,xsout,npols)
        call ortho2arrmove(ys15,ysout,npols)
        call ortho2arrmove(ws15,wsout,npols)
        endif
c
        if( norder .eq. 16 ) then
        npols=153
        call ortho2arrmove(xs16,xsout,npols)
        call ortho2arrmove(ys16,ysout,npols)
        call ortho2arrmove(ws16,wsout,npols)
        endif
c
        if( norder .eq. 17 ) then
        npols=171
        call ortho2arrmove(xs17,xsout,npols)
        call ortho2arrmove(ys17,ysout,npols)
        call ortho2arrmove(ws17,wsout,npols)
        endif
c
        if( norder .eq. 18 ) then
        npols=190
        call ortho2arrmove(xs18,xsout,npols)
        call ortho2arrmove(ys18,ysout,npols)
        call ortho2arrmove(ws18,wsout,npols)
        endif
c
        if( norder .eq. 19 ) then
        npols=210
        call ortho2arrmove(xs19,xsout,npols)
        call ortho2arrmove(ys19,ysout,npols)
        call ortho2arrmove(ws19,wsout,npols)
        endif
c
        if( norder .eq. 20 ) then
        npols=231
        call ortho2arrmove(xs20,xsout,npols)
        call ortho2arrmove(ys20,ysout,npols)
        call ortho2arrmove(ws20,wsout,npols)
        endif
c
c
c       on the standard triangle, the sum of the weights should be
c       sqrt(3.0d0)  
c       
        d=0
        do 1200 i=1,npols
        d=d+wsout(i)
 1200 continue
c
cccc        call prin2('in ortho2smexps, sum of weights=*',d,1)
c
        do 1400 i=1,npols
        wsout(i)=wsout(i)/d
        wsout(i)=wsout(i)*sqrt(3.0d0)
 1400 continue
c
c       get the interpolation matrices
c
        call ortho2intpmatr(norder,xsout,ysout,npols,umatr,vmatr)
c
        return
        end
c
c
c
c
c
        subroutine ortho2smexps_old(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
        implicit real *8 (a-h,o-z)
        dimension xs0(1),ys0(1),ws0(1)
        dimension xs1(3),ys1(3),ws1(3)
        dimension xs2(6),ys2(6),ws2(6)
        dimension xs3(10),ys3(10),ws3(10)
        dimension xs4(15),ys4(15),ws4(15)
        dimension xs5(21),ys5(21),ws5(21)
        dimension xs6(28),ys6(28),ws6(28)
        dimension xs7(36),ys7(36),ws7(36)
        dimension xs8(45),ys8(45),ws8(45)
        dimension xsout(1),ysout(1),wsout(1),umatr(1),vmatr(1)
c
c       This subroutine constructs (or rather retrieves) the
c       interpolation nodes for the polynomials (i.e. smooth functions)
c       on the standard triangle with the vertices
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))            (1)
c
c       and the corresponding quadrature weights. It also constructs the
c       matrix vmatr converting the coefficients of the polynomial
c       expansion to its values at the interpolation nodes, and its
c       inverse umatr, converting the values of a function at the
c       interpolation nodes into the coefficients of the polynomial
c       expansion.
c
c       The tables are valid up to order 8.
c       
c
c         Input parameters:
c
c    itype - the type of the calculation to be performed. currently
c          unused
c    norder - the order of the expansion
c
c
c         Output parameters:
c
c    npols - the number of the polynomials, i.e. the terms in the
c          expansion
c    xsout - the x-coordinates of the interpolation nodes (npols of them)
c    ysout - the y-coordinates of the interpolation nodes (npols of them)
c    umatr - the npols*npols matrix, converting the values of the polynomial
c          at the interpolation nodes into the coefficients of its expansion
c    vmatr - the npols*npols matrix, converting the coefficients of 
c          the expansion into its values at the interpolation nodes.
c    wsout - the corresponding quadrature weigths (npols of them)
c
c
c       NOTE: the nodes are fully symmetric only for the orders 
c       0, 1, 2, 3, 4, and 6.
c       
c
c
c       ... interpolation of order 0, quadratures of order 1
c
        data xs0/
     1  0.0000000000000000D+00/
c
        data ys0/
     2  0.0000000000000000D+00/
c
        data ws0/
     3  0.4559014113909554D+01/
c
c       ... interpolation of order 1, quadratures of order 2
c
        data xs1/
     1  -.3402060691549643D-17,-.5000000000000001D+00,
     2  0.4999999999999999D+00/
c
        data ys1/
     3  0.5773502691896258D+00,-.2886751345948128D+00,
     4  -.2886751345948131D+00/
c
        data ws1/
     5  0.1519671371303185D+01,0.1519671371303185D+01,
     6  0.1519671371303185D+01/
c
c       ... interpolation of order 2, quadratures of order 4
c
        data xs2/
     1  0.0000000000000000D+00,0.3378454727478947D+00,
     2  -.3378454727478947D+00,0.0000000000000000D+00,
     3  -.7252713594706878D+00,0.7252713594706878D+00/
c
        data ys2/
     5  -.3901103492709867D+00,0.1950551746354934D+00,
     6  0.1950551746354934D+00,0.8374712292518548D+00,
     7  -.4187356146259274D+00,-.4187356146259274D+00/
c
        data ws2/
     9  0.5091999100648037D+00,0.5091999100648037D+00,
     *  0.5091999100648037D+00,0.2506357755867889D+00,
     1  0.2506357755867889D+00,0.2506357755867889D+00/
c
c       ... interpolation of order 3, quadratures of order 5
c
        data xs3/
     1  -.7342772058729118D+00,0.6560067324471173D+00,
     2  0.7827047342579452D-01,0.7342772058729118D+00,
     3  -.7827047342579452D-01,-.6560067324471173D+00,
     4  0.0000000000000000D+00,0.3808440693425543D+00,
     5  -.3808440693425543D+00,0.0000000000000000D+00/
c
        data ys3/
     7  -.3335561846665681D+00,-.4691246213725138D+00,
     8  0.8026808060390819D+00,-.3335561846665681D+00,
     9  0.8026808060390819D+00,-.4691246213725138D+00,
     *  -.4397608519083925D+00,0.2198804259541962D+00,
     1  0.2198804259541962D+00,0.0000000000000000D+00/
c
        data ws3/
     3  0.1448211723381508D+00,0.1448211723381508D+00,
     4  0.1448211723381508D+00,0.1448211723381508D+00,
     5  0.1448211723381508D+00,0.1448211723381508D+00,
     6  0.3355329922134641D+00,0.3355329922134641D+00,
     7  0.3355329922134641D+00,0.4039810462854807D+00/
c
c       ... interpolation of order 4, quadratures of order 7
c
        data xs4/
     1  0.0000000000000000D+00,-.8725503636530545D+00,
     2  0.8725503636530545D+00,0.0000000000000000D+00,
     3  0.4228790148176862D+00,-.4228790148176862D+00,
     4  -.5276838455327671D+00,0.6918311610694409D+00,
     5  -.1641473155366737D+00,0.5276838455327671D+00,
     6  0.1641473155366737D+00,-.6918311610694409D+00,
     7  0.0000000000000000D+00,-.2737020529931245D+00,
     8  0.2737020529931245D+00/
c
        data ys4/
     9  0.1007534374673194D+01,-.5037671873365969D+00,
     *  -.5037671873365969D+00,-.4882986260792698D+00,
     1  0.2441493130396349D+00,0.2441493130396349D+00,
     2  -.4941994038890660D+00,-.2098879134535071D+00,
     3  0.7040873173425731D+00,-.4941994038890660D+00,
     4  0.7040873173425731D+00,-.2098879134535071D+00,
     5  0.3160439079466673D+00,-.1580219539733337D+00,
     6  -.1580219539733337D+00/
c
        data ws4/
     7  0.5235344496561399D-01,0.5235344496561399D-01,
     8  0.5235344496561399D-01,0.1657491147295457D+00,
     9  0.1657491147295457D+00,0.1657491147295457D+00,
     *  0.1259490797475963D+00,0.1259490797475963D+00,
     1  0.1259490797475963D+00,0.1259490797475963D+00,
     2  0.1259490797475963D+00,0.1259490797475963D+00,
     3  0.2898349664612402D+00,0.2898349664612402D+00,
     4  0.2898349664612402D+00/
c
c       ... interpolation of order 5, quadratures of order 9
c
        data xs5/
     1  -.2879034948781018D+00,0.5869272848532110D+00,
     2  -.2990237899751090D+00,-.5904715201372642D+00,
     3  0.7328093388942800D+00,-.1423378187570155D+00,
     4  0.6078058010423891D+00,0.1587394264466923D+00,
     5  -.7665452274890812D+00,-.8771723974844249D+00,
     6  0.8831360952314307D+00,-.5963697747005392D-02,
     7  -.5553614900809978D-01,0.2434289573805245D+00,
     8  -.1878928083724246D+00,0.4504610872757508D+00,
     9  0.4790286327471319D-01,-.4983639505504639D+00,
     *  0.1406401086124484D+00,0.3745241777094893D+00,
     *  -.5151642863219376D+00/
c        
        data ys5/
     *  -.5115040915409690D+00,0.6420305367725199D-02,
     *  0.5050837861732437D+00,-.5052664470505116D+00,
     *  -.2587301131248299D+00,0.7639965601753413D+00,
     *  -.5342133440268485D+00,0.7934819362836834D+00,
     *  -.2592685922568346D+00,-.5133220048125410D+00,
     *  -.5029925773137429D+00,0.1016314582126284D+01,
     *  -.2490237375648100D+00,0.7641615291303257D-01,
     *  0.1726075846517774D+00,-.3153872920113250D+00,
     *  0.5478043910028219D+00,-.2324170989914966D+00,
     *  -.5136618742034490D+00,0.3786288439511074D+00,
     *  0.1350330302523418D+00/
c
        data ws5/
     *  0.1519532255725797D+00,0.1519532255725797D+00,
     *  0.1519532255725797D+00,0.1469219802163211D+00,
     *  0.1469219802163211D+00,0.1469219802163211D+00,
     *  0.1221762882256253D+00,0.1221762882256253D+00,
     *  0.1221762882256253D+00,0.9010698462934753D-01,
     *  0.9010698462934753D-01,0.9010698462934753D-01,
     *  0.4581969425656957D+00,0.4581969425656957D+00,
     *  0.4581969425656957D+00,0.3456282846321344D+00,
     *  0.3456282846321344D+00,0.3456282846321344D+00,
     *  0.2046876654614801D+00,0.2046876654614801D+00,
     *  0.2046876654614801D+00/
c
c       ... interpolation of order 6, quadratures of order 10
c
        data xs6/
     1  -.6970050189800155D+00,0.8163460245057595D+00,
     2  -.1193410055257440D+00,0.6970050189800155D+00,
     3  0.1193410055257440D+00,-.8163460245057595D+00,
     4  -.2211000255164651D+00,0.3895271748634169D+00,
     5  -.1684271493469518D+00,0.2211000255164651D+00,
     6  0.1684271493469518D+00,-.3895271748634169D+00,
     7  -.3849378874153524D+00,0.6475290152671817D+00,
     8  -.2625911278518294D+00,0.3849378874153524D+00,
     9  0.2625911278518294D+00,-.6475290152671817D+00,
     *  0.0000000000000000D+00,0.4563731941990658D+00,
     1  -.4563731941990658D+00,0.0000000000000000D+00,
     2  -.6158294745366677D+00,0.6158294745366677D+00,
     3  0.0000000000000000D+00,-.9095920329874295D+00,
     4  0.9095920329874295D+00,0.0000000000000000D+00/
c
        data ys6/
     6  -.5402191586659300D+00,-.3335144736689832D+00,
     7  0.8737336323349132D+00,-.5402191586659300D+00,
     8  0.8737336323349132D+00,-.3335144736689832D+00,
     9  -.3221350792783721D+00,-.3041069923546031D-01,
     *  0.3525457785138324D+00,-.3221350792783721D+00,
     1  0.3525457785138324D+00,-.3041069923546031D-01,
     2  -.5254581096246618D+00,-.7063693456847844D-01,
     3  0.5960950441931402D+00,-.5254581096246618D+00,
     4  0.5960950441931402D+00,-.7063693456847844D-01,
     5  -.5269743730435200D+00,0.2634871865217600D+00,
     6  0.2634871865217600D+00,0.7110986257973017D+00,
     7  -.3555493128986509D+00,-.3555493128986509D+00,
     8  0.1050306410196063D+01,-.5251532050980314D+00,
     9  -.5251532050980314D+00,0.0000000000000000D+00/
c
        data ws6/
     1  0.3566346022748086D-01,0.3566346022748086D-01,
     2  0.3566346022748086D-01,0.3566346022748086D-01,
     3  0.3566346022748086D-01,0.3566346022748086D-01,
     4  0.1537711927527378D+00,0.1537711927527378D+00,
     5  0.1537711927527378D+00,0.1537711927527378D+00,
     6  0.1537711927527378D+00,0.1537711927527378D+00,
     7  0.5963474204157574D-01,0.5963474204157574D-01,
     8  0.5963474204157574D-01,0.5963474204157574D-01,
     9  0.5963474204157574D-01,0.5963474204157574D-01,
     *  0.6881925595930596D-01,0.6881925595930596D-01,
     1  0.6881925595930596D-01,0.1043099501289462D+00,
     2  0.1043099501289462D+00,0.1043099501289462D+00,
     3  0.2574634864641487D-01,0.2574634864641487D-01,
     4  0.2574634864641487D-01,0.1884640226200104D+00/
c
c       ... interpolation of order 7, quadratures of order 13
c
        data xs7/
     1  -.1734921014384450D-01,0.1675838485269257D+00,
     2  -.1502346383830812D+00,-.3257509002404932D+00,
     3  0.3016835664569898D+00,0.2406733378350348D-01,
     4  -.2042415343626712D-01,0.4832529946042317D+00,
     5  -.4628288411679644D+00,0.3948715670808531D+00,
     6  0.1571611895246048D+00,-.5520327566054578D+00,
     7  -.7312664063197668D+00,0.8360664633170760D+00,
     8  -.1048000569973090D+00,0.3802568182919678D+00,
     9  0.2813989891257929D+00,-.6616558074177605D+00,
     *  -.3478853768686158D+00,0.5134495579307109D+00,
     1  -.1655641810620950D+00,-.4087860152682592D+00,
     2  0.6719507745444188D+00,-.2631647592761593D+00,
     3  -.6609371532209790D+00,0.6733670469640336D+00,
     4  -.1242989374305437D-01,0.2364343818548231D-01,
     5  0.3473902844994198D+00,-.3710337226849019D+00,
     6  0.7171575469189121D+00,0.1079608700314365D+00,
     7  -.8251184169503485D+00,-.9253514478845177D+00,
     8  0.9242023578994309D+00,0.1149089985087004D-02/
c        
        data ys7/
     *  -.1834925889709321D+00,0.7672143776530198D-01,
     1  0.1067711512056301D+00,-.1602818066654472D+00,
     2  -.2019676515811940D+00,0.3622494582466411D+00,
     3  -.5462206025584928D+00,0.2554224655526477D+00,
     4  0.2907981370058451D+00,-.4094533157058446D+00,
     5  0.5466954661771121D+00,-.1372421504712673D+00,
     6  -.5432095387750170D+00,-.3616905154195630D+00,
     7  0.9049000541945798D+00,-.5444729406449883D+00,
     8  0.6015485349255814D+00,-.5707559428059292D-01,
     9  -.3920287649909509D+00,-.1052631914778692D+00,
     *  0.4972919564688201D+00,-.5398892051747115D+00,
     1  -.8407447134677026D-01,0.6239636765214818D+00,
     2  -.3959450483266593D+00,-.3744158408310062D+00,
     3  0.7703608891576653D+00,-.4147822939401578D+00,
     4  0.2278669650715135D+00,0.1869153288686443D+00,
     5  -.5387135775141975D+00,0.8904334429046070D+00,
     6  -.3517198653904092D+00,-.5329250527067106D+00,
     7  -.5349153349433492D+00,0.1067840387650060D+01/
c        
        data ws7/
     9  0.2299507991422753D+00,0.2299507991422753D+00,
     *  0.2299507991422753D+00,0.1879979645110639D+00,
     1  0.1879979645110639D+00,0.1879979645110639D+00,
     2  0.8541986655788668D-01,0.8541986655788668D-01,
     3  0.8541986655788668D-01,0.1612184424444836D+00,
     4  0.1612184424444836D+00,0.1612184424444836D+00,
     5  0.6212600156028678D-01,0.6212600156028678D-01,
     6  0.6212600156028678D-01,0.8421986801721809D-01,
     7  0.8421986801721809D-01,0.8421986801721809D-01,
     8  0.1823561575587639D+00,0.1823561575587639D+00,
     9  0.1823561575587639D+00,0.9100634002058296D-01,
     *  0.9100634002058296D-01,0.9100634002058296D-01,
     1  0.1389110306339348D+00,0.1389110306339348D+00,
     2  0.1389110306339348D+00,0.1862000629703836D+00,
     3  0.1862000629703836D+00,0.1862000629703836D+00,
     4  0.7320797987119952D-01,0.7320797987119952D-01,
     5  0.7320797987119952D-01,0.3705685801510442D-01,
     6  0.3705685801510442D-01,0.3705685801510442D-01/
c        
c       ... interpolation of order 8, quadratures of order 14
c
        data xs8/
     1  0.5392743522783505D+00,0.2084645620209433D+00,
     2  -.7477389142992936D+00,-.4388045073864397D-01,
     3  0.5069210101200965D+00,-.4630405593814523D+00,
     4  0.8409138230263630D+00,-.3369927369312320D-01,
     5  -.8072145493332398D+00,-.7039847068812235D+00,
     6  0.8391891611726698D+00,-.1352044542914461D+00,
     7  0.1261699049844250D+00,0.2733943663737719D+00,
     8  -.3995642713581968D+00,0.8290725673809252D+00,
     9  0.7347786396479916D-01,-.9025504313457242D+00,
     *  0.9533632917085324D+00,-.9547868047188213D-02,
     1  -.9438154236613441D+00,0.6150807756135514D-01,
     2  0.1203425522238438D+00,-.1818506297851989D+00,
     3  -.1580088857546108D+00,0.4674239501161907D+00,
     4  -.3094150643615797D+00,0.6740726399906883D+00,
     5  0.7252413012069769D-01,-.7465967701113858D+00,
     6  -.2821211331054279D+00,0.3665692628510035D+00,
     7  -.8444812974557550D-01,0.2554286331982036D+00,
     8  0.3301664346372928D+00,-.5855950678354962D+00,
     9  0.4224944490571427D+00,0.1123898752131720D+00,
     *  -.5348843242703145D+00,-.4026168643831402D+00,
     1  0.6726031500275402D+00,-.2699862856443997D+00,
     2  -.5460071664916822D+00,0.6468488480175678D+00,
     3  -.1008416815258853D+00/
c
        data ys8/
     4  -.5520643344535446D+00,0.7430574559092223D+00,
     5  -.1909931214556775D+00,-.5600075732553113D+00,
     6  0.2420022015584782D+00,0.3180053716968331D+00,
     7  -.4465892526131087D+00,0.9515473594408763D+00,
     8  -.5049581068277673D+00,-.5625664161848603D+00,
     9  -.3283854319424513D+00,0.8909518481273113D+00,
     *  -.3885328506480359D+00,0.3035327682335988D+00,
     1  0.8500008241443724D-01,-.5635101990342221D+00,
     2  0.9997530044497780D+00,-.4362428054155555D+00,
     3  -.5393996247289663D+00,0.1095336642019626D+01,
     4  -.5559370172906597D+00,-.1744713149801904D+00,
     5  0.1405032151961723D+00,0.3396809978401812D-01,
     6  -.4485082141257445D+00,0.8741439797570608D-01,
     7  0.3610938161500384D+00,-.4729196722478419D+00,
     8  0.8202238663518993D+00,-.3473041941040571D+00,
     9  -.2603950130248381D+00,-.1141265617013325D+00,
     *  0.3745215747261706D+00,-.5287151499661609D+00,
     1  0.4855652601866619D+00,0.4314988977949913D-01,
     2  -.3737039333112904D+00,0.5527428924970410D+00,
     3  -.1790389591857505D+00,-.5442042644204922D+00,
     4  -.7657430033758761D-01,0.6207785647580797D+00,
     5  -.4316793285024467D+00,-.2570164125789331D+00,
     6  0.6886957410813797D+00/
c
        data ws8/
     7  0.5184823261020631D-01,0.5184823261020631D-01,
     8  0.5184823261020631D-01,0.4950578742136484D-01,
     9  0.4950578742136484D-01,0.4950578742136484D-01,
     *  0.5310054200699969D-01,0.5310054200699969D-01,
     1  0.5310054200699969D-01,0.3178186833114997D-01,
     2  0.3178186833114997D-01,0.3178186833114997D-01,
     3  0.1410377080685789D+00,0.1410377080685789D+00,
     4  0.1410377080685789D+00,0.2544794411310312D-01,
     5  0.2544794411310312D-01,0.2544794411310312D-01,
     6  0.1710801079719154D-01,0.1710801079719154D-01,
     7  0.1710801079719154D-01,0.2355757336102695D+00,
     8  0.2355757336102695D+00,0.2355757336102695D+00,
     9  0.1466686511742485D+00,0.1466686511742485D+00,
     *  0.1466686511742485D+00,0.8671140224962312D-01,
     1  0.8671140224962312D-01,0.8671140224962312D-01,
     2  0.2114874479707131D+00,0.2114874479707131D+00,
     3  0.2114874479707131D+00,0.9135931666336268D-01,
     4  0.9135931666336268D-01,0.9135931666336268D-01,
     5  0.1652301204866729D+00,0.1652301204866729D+00,
     6  0.1652301204866729D+00,0.7210145943146058D-01,
     7  0.7210145943146058D-01,0.7210145943146058D-01,
     8  0.1407071463682392D+00,0.1407071463682392D+00,
     9  0.1407071463682392D+00/
c
c
        npols=0
c        
        if( norder .eq. 0 ) then
        npols=1
        call ortho2arrmove(xs0,xsout,npols)
        call ortho2arrmove(ys0,ysout,npols)
        call ortho2arrmove(ws0,wsout,npols)
        endif
c
        if( norder .eq. 1 ) then
        npols=3
        call ortho2arrmove(xs1,xsout,npols)
        call ortho2arrmove(ys1,ysout,npols)
        call ortho2arrmove(ws1,wsout,npols)
        endif
c
        if( norder .eq. 2 ) then
        npols=6
        call ortho2arrmove(xs2,xsout,npols)
        call ortho2arrmove(ys2,ysout,npols)
        call ortho2arrmove(ws2,wsout,npols)
        endif
c
        if( norder .eq. 3 ) then
        npols=10
        call ortho2arrmove(xs3,xsout,npols)
        call ortho2arrmove(ys3,ysout,npols)
        call ortho2arrmove(ws3,wsout,npols)
        endif
c
        if( norder .eq. 4 ) then
        npols=15
        call ortho2arrmove(xs4,xsout,npols)
        call ortho2arrmove(ys4,ysout,npols)
        call ortho2arrmove(ws4,wsout,npols)
        endif
c
        if( norder .eq. 5 ) then
        npols=21
        call ortho2arrmove(xs5,xsout,npols)
        call ortho2arrmove(ys5,ysout,npols)
        call ortho2arrmove(ws5,wsout,npols)
        endif
c
        if( norder .eq. 6 ) then
        npols=28
        call ortho2arrmove(xs6,xsout,npols)
        call ortho2arrmove(ys6,ysout,npols)
        call ortho2arrmove(ws6,wsout,npols)
        endif
c
        if( norder .eq. 7 ) then
        npols=36
        call ortho2arrmove(xs7,xsout,npols)
        call ortho2arrmove(ys7,ysout,npols)
        call ortho2arrmove(ws7,wsout,npols)
        endif
c
        if( norder .eq. 8 ) then
        npols=45
        call ortho2arrmove(xs8,xsout,npols)
        call ortho2arrmove(ys8,ysout,npols)
        call ortho2arrmove(ws8,wsout,npols)
        endif

c
c       on the standard triangle, the sum of the weights should be
c       sqrt(3.0d0)  
c       
        d=0
        do 1200 i=1,npols
        d=d+wsout(i)
 1200 continue
c
cccc        call prin2('in ortho2smexps, sum of weights=*',d,1)
c
        do 1400 i=1,npols
        wsout(i)=wsout(i)/d
        wsout(i)=wsout(i)*sqrt(3.0d0)
 1400 continue
c
c       get the interpolation matrices
c
        call ortho2intpmatr(norder,xsout,ysout,npols,umatr,vmatr)
c
        return
        end
c
c
c
c
c
        subroutine ortho2sfexps_old(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
        implicit real *8 (a-h,o-z)
        dimension xs0(1),ys0(1),ws0(1)
        dimension xs1(3),ys1(3),ws1(3)
        dimension xs2(6),ys2(6),ws2(6)
        dimension xs3(10),ys3(10),ws3(10)
        dimension xs4(15),ys4(15),ws4(15)
        dimension xs5(21),ys5(21),ws5(21)
        dimension xs6(28),ys6(28),ws6(28)
        dimension xsout(1),ysout(1),wsout(1),umatr(1),vmatr(1)
c
c       This subroutine constructs (or rather retrieves) the
c       interpolation nodes for the polynomials (i.e. smooth functions)
c       on the standard triangle with the vertices
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))            (1)
c
c       and the corresponding quadrature weights. It also constructs the
c       matrix vmatr converting the coefficients of the polynomial
c       expansion to its values at the interpolation nodes, and its
c       inverse umatr, converting the values of a function at the
c       interpolation nodes into the coefficients of the polynomial
c       expansion.
c       
c       The constructed nodes are as far away from the boundary as
c       reasonably possible.  The nodes are fully symmetric and the
c       corresponding quadrature weigths are positive. The quadrature is
c       of low order and will integrate only the polynomials itself but
c       not their pairwise products (user beware).
c
c       The tables are valid up to order 6.
c       
c
c
c         Input parameters:
c
c    itype - the type of the calculation to be performed. currently
c          unused
c    norder - the order of the expansion
c
c
c         Output parameters:
c
c    npols - the number of the polynomials, i.e. the terms in the
c          expansion
c    xsout - the x-coordinates of the interpolation nodes (npols of them)
c    ysout - the y-coordinates of the interpolation nodes (npols of them)
c    umatr - the npols*npols matrix, converting the values of the polynomial
c          at the interpolation nodes into the coefficients of its expansion
c    vmatr - the npols*npols matrix, converting the coefficients of 
c          the expansion into its values at the interpolation nodes.
c    wsout - the corresponding quadrature weigths (npols of them)
c
c
c
c       ... interpolation of order 0, quadratures of order 1
c
        data xs0/
     1  0.0000000000000000D+00/
c
        data ys0/
     2  0.0000000000000000D+00/
c
        data ws0/
     3  0.4559014113909554D+01/
c
c       ... interpolation of order 1, quadratures of order 1
c
c  Data for   3 nodes
c
c        distance = .5
c
        data xs1/
     1  0.0000000000000000D+00,-.5000000000000001D+00,
     2  0.4999999999999999D+00/
c
        data ys1/
     1  0.5773502691896258D+00,-.2886751345948128D+00,
     2  -.2886751345948131D+00/
c
        data ws1/
     1  0.4386913376508305D+00,0.4386913376508308D+00,
     2  0.4386913376508309D+00/
c
c       ... interpolation of order 2, quadratures of order 2
c
c  Data for   6 nodes
c        
c        distance = .53
c
        data xs2/
     1  0.0000000000000000D+00,-.5300000000000001D+00,
     2  0.5299999999999999D+00,-.2650000000000000D+00,
     3  -.5551115123125783D-16,0.2650000000000000D+00/
c
        data ys2/
     1  0.6119912853410034D+00,-.3059956426705016D+00,
     2  -.3059956426705019D+00,0.1529978213352508D+00,
     3  -.3059956426705017D+00,0.1529978213352507D+00/
c
        data ws2/
     1  0.3743478591488220D+00,0.3743478591488221D+00,
     2  0.3743478591488218D+00,0.6434347850200858D-01,
     3  0.6434347850200872D-01,0.6434347850200892D-01/
c
c       ... interpolation of order 3, quadratures of order 3
c
c  Data for  10 nodes
c        
c        distance = .68
c
        data xs3/
     1  -.6800000000000000D+00,0.6799999999999999D+00,
     2  0.2775557561562891D-15,-.3164356435643564D+00,
     3  0.4982178217821783D+00,-.1817821782178217D+00,
     4  0.3164356435643564D+00,0.1817821782178220D+00,
     5  -.4982178217821784D+00,-.6732673267326740D-02/
c
        data ys3/
     1  -.3925981830489457D+00,-.3925981830489456D+00,
     2  0.7851963660978909D+00,-.3925981830489457D+00,
     3  -.7774221446513777D-01,0.4703403975140834D+00,
     4  -.3925981830489457D+00,0.4703403975140833D+00,
     5  -.7774221446513743D-01,0.3887110723256777D-02/
c
        data ws3/
     1  0.1001316929310150D+00,0.1000027750773283D+00,
     2  0.1001316929310150D+00,0.1661504331210198D+00,
     3  0.1663721411523347D+00,0.1661034041446803D+00,
     4  0.1663721411523346D+00,0.1661504331210194D+00,
     5  0.1661034041446801D+00,0.1855589517706505D-01/
c
c       ... interpolation of order 4, quadratures of order 4
c        
c  Data for  15 nodes
c        
c        distance = .75
c
        data xs4/
     1  -.7500000000000000D+00,0.7500000000000000D+00,
     2  0.2220446049250313D-15,-.4950000000000000D+00,
     3  0.6225000000000002D+00,-.1275000000000000D+00,
     4  0.4950000000000000D+00,0.1275000000000004D+00,
     5  -.6225000000000003D+00,0.0000000000000000D+00,
     6  0.3750000000000002D+00,-.3750000000000000D+00,
     7  0.7425742574257432D-02,-.2747524752475248D+00,
     8  0.2673267326732672D+00/
c
        data ys4/
     1  -.4330127018922195D+00,-.4330127018922194D+00,
     2  0.8660254037844386D+00,-.4330127018922196D+00,
     3  -.2121762239271874D+00,0.6451889258194069D+00,
     4  -.4330127018922196D+00,0.6451889258194069D+00,
     5  -.2121762239271870D+00,-.4330127018922195D+00,
     6  0.2165063509461096D+00,0.2165063509461099D+00,
     7  0.3129695766151684D+00,-.1500539065963135D+00,
     8  -.1629156700188549D+00/
c
        data ws4/
     1  0.1134953065507076D+00,0.1134953065507077D+00,
     2  0.1134953065507078D+00,0.1694230042014065D-01,
     3  0.1694230042014019D-01,0.1694230042014065D-01,
     4  0.1572168617610268D-01,0.1572168617610206D-01,
     5  0.1572168617610268D-01,0.2046076716055766D+00,
     6  0.2046076716055767D+00,0.2046076716055766D+00,
     7  0.8792437289830354D-01,0.8792437289830318D-01,
     8  0.8792437289830336D-01/
c
c       ... interpolation of order 5, quadratures of order 5
c        
c  Data for  21 nodes
c        
c        distance = .85
c
        data xs5/
     1  -.8500000000000000D+00,0.8500000000000000D+00,
     2  0.2220446049250313D-15,-.6460000000000000D+00,
     3  0.7480000000000000D+00,-.1019999999999997D+00,
     4  0.6460000000000000D+00,0.1020000000000003D+00,
     5  -.7480000000000001D+00,-.2440594059405941D+00,
     6  0.5470297029702971D+00,-.3029702970297028D+00,
     7  0.2440594059405941D+00,0.3029702970297031D+00,
     8  -.5470297029702971D+00,-.4675000000000000D+00,
     9  0.4675000000000000D+00,0.1387778780781446D-15,
     *  -.8415841584158423D-02,0.2272277227722773D+00,
     *  -.2188118811881188D+00/
c        
        data ys5/
     1  -.4907477288111821D+00,-.4907477288111819D+00,
     2  0.9814954576223637D+00,-.4907477288111819D+00,
     3  -.3140785464391566D+00,0.8048262752503383D+00,
     4  -.4907477288111819D+00,0.8048262752503382D+00,
     5  -.3140785464391560D+00,-.4907477288111819D+00,
     6  0.3401221882849764D-01,0.4567355099826843D+00,
     7  -.4907477288111819D+00,0.4567355099826841D+00,
     8  0.3401221882849803D-01,-.2699112508461502D+00,
     9  -.2699112508461501D+00,0.5398225016923002D+00,
     *  -.2575210854157688D+00,0.1214722101017777D+00,
     *  0.1360488753139912D+00/
c
        data ws5/
     1  0.2205448166752153D-01,0.2205448166752149D-01,
     2  0.2205448166752149D-01,0.4780154212294979D-01,
     3  0.4780154212294977D-01,0.4780154212294993D-01,
     4  0.4700114109582408D-01,0.4700114109582394D-01,
     5  0.4700114109582395D-01,0.6759874001906731D-01,
     6  0.6759874001906717D-01,0.6759874001906728D-01,
     7  0.7006504569617590D-01,0.7006504569617572D-01,
     8  0.7006504569617569D-01,0.4003922816302670D-01,
     9  0.4003922816302631D-01,0.4003922816302625D-01,
     *  0.1441311588862657D+00,0.1441311588862662D+00,
     *  0.1441311588862660D+00/
c
c       ... interpolation of order 6, quadratures of order 6
c        
c  Data for  28 nodes
c        
c        distance = .89
c
        data xs6/
     1  -.8900000000000000D+00,0.8899999999999999D+00,
     2  0.3885780586188048D-15,-.7313861386138615D+00,
     3  0.8106930693069310D+00,-.7930693069306921D-01,
     4  0.7313861386138615D+00,0.7930693069306982D-01,
     5  -.8106930693069312D+00,-.4141584158415841D+00,
     6  0.6520792079207922D+00,-.2379207920792078D+00,
     7  0.4141584158415841D+00,0.2379207920792082D+00,
     8  -.6520792079207922D+00,0.0000000000000000D+00,
     9  0.4450000000000002D+00,-.4450000000000000D+00,
     *  0.0000000000000000D+00,-.5963000000000002D+00,
     1  0.5962999999999998D+00,-.2291089108910891D+00,
     2  0.4141584158415842D+00,-.1850495049504950D+00,
     3  0.2291089108910891D+00,0.1850495049504952D+00,
     4  -.4141584158415841D+00,0.0000000000000000D+00/
c
        data ys6/
     1  -.5138417395787671D+00,-.5138417395787670D+00,
     2  0.1027683479157534D+01,-.5138417395787673D+00,
     3  -.3764781062260273D+00,0.8903198458047944D+00,
     4  -.5138417395787673D+00,0.8903198458047944D+00,
     5  -.3764781062260267D+00,-.5138417395787671D+00,
     6  -.1017508395205479D+00,0.6155925790993150D+00,
     7  -.5138417395787671D+00,0.6155925790993149D+00,
     8  -.1017508395205476D+00,-.5138417395787671D+00,
     9  0.2569208697893834D+00,0.2569208697893837D+00,
     *  0.6885479310355478D+00,-.3442739655177737D+00,
     1  -.3442739655177741D+00,-.3459528543698629D+00,
     2  -.2543770988013699D-01,0.3713905642499999D+00,
     3  -.3459528543698629D+00,0.3713905642499998D+00,
     4  -.2543770988013669D-01,0.0000000000000000D+00/
c
        data ws6/
     1  0.2207730458237053D-01,0.2207730458237058D-01,
     2  0.2207730458237056D-01,0.1237260769490342D-01,
     3  0.1237260769490339D-01,0.1237260769490354D-01,
     4  0.1237260769490334D-01,0.1237260769490325D-01,
     5  0.1237260769490349D-01,0.5116764587531173D-01,
     6  0.5116764587531177D-01,0.5116764587531177D-01,
     7  0.5116764587531177D-01,0.5116764587531182D-01,
     8  0.5116764587531157D-01,0.3642644935718405D-01,
     9  0.3642644935718384D-01,0.3642644935718404D-01,
     *  0.5020415030954761D-01,0.5020415030954779D-01,
     1  0.5020415030954774D-01,0.7303862873731552D-01,
     2  0.7303862873731545D-01,0.7303862873731531D-01,
     3  0.7303862873731534D-01,0.7303862873731555D-01,
     4  0.7303862873731559D-01,0.1704770063600019D+00/
c
c
        npols=0
c        
        if( norder .eq. 0 ) then
        npols=1
        call ortho2arrmove(xs0,xsout,npols)
        call ortho2arrmove(ys0,ysout,npols)
        call ortho2arrmove(ws0,wsout,npols)
        endif
c
        if( norder .eq. 1 ) then
        npols=3
        call ortho2arrmove(xs1,xsout,npols)
        call ortho2arrmove(ys1,ysout,npols)
        call ortho2arrmove(ws1,wsout,npols)
        endif
c
        if( norder .eq. 2 ) then
        npols=6
        call ortho2arrmove(xs2,xsout,npols)
        call ortho2arrmove(ys2,ysout,npols)
        call ortho2arrmove(ws2,wsout,npols)
        endif
c
        if( norder .eq. 3 ) then
        npols=10
        call ortho2arrmove(xs3,xsout,npols)
        call ortho2arrmove(ys3,ysout,npols)
        call ortho2arrmove(ws3,wsout,npols)
        endif
c
        if( norder .eq. 4 ) then
        npols=15
        call ortho2arrmove(xs4,xsout,npols)
        call ortho2arrmove(ys4,ysout,npols)
        call ortho2arrmove(ws4,wsout,npols)
        endif
c
        if( norder .eq. 5 ) then
        npols=21
        call ortho2arrmove(xs5,xsout,npols)
        call ortho2arrmove(ys5,ysout,npols)
        call ortho2arrmove(ws5,wsout,npols)
        endif
c
        if( norder .eq. 6 ) then
        npols=28
        call ortho2arrmove(xs6,xsout,npols)
        call ortho2arrmove(ys6,ysout,npols)
        call ortho2arrmove(ws6,wsout,npols)
        endif
c
c
c       on the standard triangle, the sum of the weights should be
c       sqrt(3.0d0)  
c       
        d=0
        do 1200 i=1,npols
        d=d+wsout(i)
 1200 continue
c
cccc        call prin2('in ortho2smexps, sum of weights=*',d,1)
c
        do 1400 i=1,npols
        wsout(i)=wsout(i)/d
        wsout(i)=wsout(i)*sqrt(3.0d0)
 1400 continue
c
c       get the interpolation matrices
c
        call ortho2intpmatr(norder,xsout,ysout,npols,umatr,vmatr)
c
        return
        end
c
c
c
c
c
        subroutine ortho2intpmatr(norder,xs,ys,npols,umatr,vmatr)
        implicit real *8 (a-h,o-z)
        dimension xs(1),ys(1),umatr(npols,npols),vmatr(npols,npols)
        dimension z(2),work(80 000)
c
c       form the interpolation matrices umatr and vmatr
c
        do 1200 i=1,npols
c
        z(1)=xs(i)
        z(2)=ys(i)
        call ortho2eva(norder,z,vmatr(1,i),work)
        call ortho2eva(norder,z,umatr(1,i),work)
 1200 continue
c
c       transpose umatr and vmatr
c
        do 1600 j=1,npols
        do 1400 i=1,npols
        if( i .gt. j ) goto 1400
c
        tmp=umatr(i,j)
        umatr(i,j)=umatr(j,i)
        umatr(j,i)=tmp
c
        tmp=vmatr(i,j)
        vmatr(i,j)=vmatr(j,i)
        vmatr(j,i)=tmp        
 1400 continue
 1600 continue
c
        call orthom(umatr,npols,work,rcond)
cccc        call prin2('rcond=*',rcond,1)
c
        return
        end
c
c       
c
c
c
        subroutine ortho2diffmatr(norder,xs,ys,npols,umatr,vmatr,
     $     dxmatr,dymatr)
        implicit real *8 (a-h,o-z)
        dimension xs(1),ys(1),umatr(npols,npols),vmatr(npols,npols),
     $     dxmatr(npols,npols),dymatr(npols,npols)
        dimension z(2),work(10 000),work2(10 000)
c
c       This subroutine constructs the matrices of spectral differentiation 
c       on the nodes (xs,ys). The nodes are located on the standard triangle 
c       with the vertices
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))            (1)
c
c       and the differentiation is perfomed with respect to x and y on
c       the said triangle
c
c       ... first, construct the interpolation matrices
c
        call ortho2intpmatr(norder,xs,ys,npols,umatr,vmatr)
c
ccc        call prin2('in diffmatr, xs=*',xs,npols)
ccc        call prin2('in diffmatr, ys=*',ys,npols)
ccc        call prin2('in diffmatr, umatr=*',umatr,npols*npols)
ccc        call prin2('in diffmatr, vmatr=*',vmatr,npols*npols)
c
        do 1200 i=1,npols
c
        z(1)=xs(i)
        z(2)=ys(i)
        call ortho2eva3(norder,z,work2,dxmatr(1,i),dymatr(1,i),work)
 1200 continue
c
c       transpose dxmatr and dymatr
c
        do 1600 j=1,npols
        do 1400 i=1,npols
        if( i .gt. j ) goto 1400
c
        tmp=dxmatr(i,j)
        dxmatr(i,j)=dxmatr(j,i)
        dxmatr(j,i)=tmp
c
        tmp=dymatr(i,j)
        dymatr(i,j)=dymatr(j,i)
        dymatr(j,i)=tmp        
 1400 continue
 1600 continue
c
        call ortho2matmul(dxmatr,umatr,work2,npols)
        call ortho2arrmove(work2,dxmatr,npols*npols)
c
        call ortho2matmul(dymatr,umatr,work2,npols)
        call ortho2arrmove(work2,dymatr,npols*npols)
c
        return
        end
c
c       
c
c
c
        subroutine ortho2siexps(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
        implicit real *8 (a-h,o-z)
        dimension xsout(1),ysout(1),wsout(1),umatr(1),vmatr(1)
c
c       This subroutine constructs the interpolation nodes for the
c       polynomials (i.e. smooth functions) on the simplex triangle with
c       the vertices 
c
c       (0,0), (1,0), (0,1)                                   (1)
c
c       and the corresponding quadrature weights. It also
c       constructs the matrix vmatr converting the coefficients of the
c       polynomial expansion to its values at the interpolation nodes,
c       and its inverse umatr, converting the values of a function at
c       the interpolation nodes into the coefficients of the polynomial
c       expansion.
c
c         Input parameters:
c
c    itype - the type of the calculation to be performed. currently
c          unused
c    norder - the order of the expansion
c
c
c         Output parameters:
c
c    npols - the number of the polynomials, i.e. the terms in the
c          expansion
c    xsout - the x-coordinates of the interpolation nodes (npols of them)
c    ysout - the y-coordinates of the interpolation nodes (npols of them)
c    umatr - the npols*npols matrix, converting the values of the polynomial
c          at the interpolation nodes into the coefficients of its expansion
c    vmatr - the npols*npols matrix, converting the coefficients of 
c          the expansion into its values at the interpolation nodes.
c    wsout - the corresponding quadrature weigths (npols of them)
c
c
c
c       ... first, get the interpolation nodes for the standard triangle
c
c
        call ortho2smexps(itype,norder,npols,xsout,ysout,
     1     umatr,vmatr,wsout)
c
ccc        call ortho2sfexps(itype,norder,npols,xsout,ysout,
ccc     1     umatr,vmatr,wsout)
c
c       ... and convert them into simplex coordinates
c
        do 1800 i=1,npols
        call ortho2_stdtosimplex(xsout(i),ysout(i),u,v)
        xsout(i)=u
        ysout(i)=v
        wsout(i)=wsout(i)/sqrt(3.0d0)
        wsout(i)=wsout(i)*0.5d0
 1800 continue
c
ccc        call prin2('xsout=*',xsout,npols)
ccc        call prin2('ysout=*',ysout,npols)
c
        return
        end
c
c
c
c
c
        subroutine ortho2sipols(u,v,norder,pols)
        implicit real *8 (a-h,o-z)
        dimension pols(1),vert1(2),vert2(2),vert3(2)
        dimension z(2),work(10 000)
c        data ifinit/0/
c        save
c
c       evaluates a bunch of orthogonal polynomials on the simplex
c       at the user-provided point
c
c
c        if( ifinit .eq. 0 ) then
c
        vert1(1)=-1
        vert1(2)=-1/sqrt(3.0d0)
        vert2(1)=1
        vert2(2)=-1/sqrt(3.0d0)
        vert3(1)=0
        vert3(2)=2/sqrt(3.0d0)
c
c        ifinit=1
c        endif
c
        x=vert1(1)+u*(vert2(1)-vert1(1))+v*(vert3(1)-vert1(1))
        y=vert1(2)+u*(vert2(2)-vert1(2))+v*(vert3(2)-vert1(2))
c
        z(1)=x
        z(2)=y
        call ortho2eva(norder,z,pols,work)
c
        return
        end
c
c
c
c
c       
        subroutine ortho2sipolders(u,v,norder,pols,dersu,dersv)
        implicit real *8 (a-h,o-z)
        dimension pols(1),dersu(1),dersv(1)
        dimension vert1(2),vert2(2),vert3(2),z(2),
     $     dersx(10 000),dersy(10 000),work(10 000)
c        data ifinit/0/
c        save
c
c       evaluates a bunch of orthogonal polynomials on the simplex at
c       the user-provided point, and the derivatives of the said
c       polynomials
c
c
c        if( ifinit .eq. 0 ) then
c
        vert1(1)=-1
        vert1(2)=-1/sqrt(3.0d0)
        vert2(1)=1
        vert2(2)=-1/sqrt(3.0d0)
        vert3(1)=0
        vert3(2)=2/sqrt(3.0d0)
c
c        ifinit=1
c        endif
c
        x=vert1(1)+u*(vert2(1)-vert1(1))+v*(vert3(1)-vert1(1))
        y=vert1(2)+u*(vert2(2)-vert1(2))+v*(vert3(2)-vert1(2))
c
        z(1)=x
        z(2)=y
        call ortho2eva3(norder,z,pols,dersx,dersy,work)
c
        npols=(norder+1)*(norder+2)/2
c
        do 1200 i=1,npols
        dersu(i)=
     $      dersx(i)*(vert2(1)-vert1(1))
     $     +dersy(i)*(vert2(2)-vert1(2))
        dersv(i)=
     $      dersx(i)*(vert3(1)-vert1(1))
     $     +dersy(i)*(vert3(2)-vert1(2))
 1200   continue
c
        return
        end
c
c
c
c
c       
        subroutine ortho2siexevc(u,v,cval,norder,npols,coefs)
        implicit real *8 (a-h,o-z)
        dimension vert1(2),vert2(2),vert3(2),z(2)
        dimension work(10 000),pols(10 000)
        complex *16 coefs(1),cval
c        data ifinit/0/
c        save
c
c       computes the value of polynomial expansion on the simplex
c       at the user-provided point
c
c
c        if( ifinit .eq. 0 ) then
c
        vert1(1)=-1
        vert1(2)=-1/sqrt(3.0d0)
        vert2(1)=1
        vert2(2)=-1/sqrt(3.0d0)
        vert3(1)=0
        vert3(2)=2/sqrt(3.0d0)
c
c        ifinit=1
c        endif
c
        x=vert1(1)+u*(vert2(1)-vert1(1))+v*(vert3(1)-vert1(1))
        y=vert1(2)+u*(vert2(2)-vert1(2))+v*(vert3(2)-vert1(2))
c
        z(1)=x
        z(2)=y
        call ortho2eva(norder,z,pols,work)
c
        cval=0
c
        do 1200 i=1,npols
        cval=cval+coefs(i)*pols(i)
 1200 continue
c
        return
        end
c
c
c
c
c
        subroutine ortho2triangle(itype,vert1,vert2,vert3)
        implicit real *8 (a-h,o-z)
        dimension vert1(2),vert2(2),vert3(2)
c
c
        if( itype .eq. 1 ) then 
c
c
c       ... construct the simplex triangle with the vertices 
c
c       (0,0), (1,0), (0,1)
c
c
        vert1(1)=0
        vert1(2)=0
        vert2(1)=1
        vert2(2)=0
        vert3(1)=0
        vert3(2)=1
c
        endif
c
        if( itype .eq. 2 ) then 
c
c
c       ... construct the standard triangle with the vertices 
c
c       (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0, 2/sqrt(3))
c
c        
        vert1(1)=-1
        vert1(2)=-1/sqrt(3.0d0)
        vert2(1)=1
        vert2(2)=-1/sqrt(3.0d0)
        vert3(1)=0
        vert3(2)=2/sqrt(3.0d0)
c
        endif
c
        return
        end
c
c
c
c
c
        subroutine ortho2arrmove(x,y,n)
        implicit real *8 (a-h,o-z)
        dimension x(1),y(1)
c
        do 1200 i=1,n
        y(i)=x(i)
 1200 continue
        return
        end
c
c
c
c
c
        subroutine ortho2matmul(a,b,c,n)
        implicit real *8 (a-h,o-z)
        dimension a(n,n),b(n,n),c(n,n)
c
        do 2000 i=1,n
        do 1800 j=1,n
        d=0
        do 1600 k=1,n
        d=d+a(i,k)*b(k,j)
 1600 continue
        c(i,j)=d
 1800 continue
 2000 continue
        return
c
c
c
c
        entry ortho2matmua(a,b,c,n)
ccc          call prin2('in matmua, a=*',a,n**2)
ccc          call prin2('in matmua, b=*',b,n**2)
        do 3000 i=1,n
        do 2800 j=1,n
        d=0
        do 2600 k=1,n
        d=d+a(i,k)*b(j,k)
 2600 continue
        c(i,j)=d
 2800 continue
 3000 continue
ccc          call prin2('exiting, c=*',c,n**2)
        return
        end
c
c
c
c
        subroutine ortho2_stdtosimplex(x,y,uout,vout)
        implicit real *8 (a-h,o-z)
c
c       map the standard triangle to the simplex
c
        sqrt3=sqrt(3.0d0)
        uout=0.5d0*(x+1)-0.5d0/sqrt3*(y+1/sqrt3)
        vout=            1.0d0/sqrt3*(y+1/sqrt3)
c
        return
        end
c
c
c
c
c
        subroutine ortho2_simplextostd(u,v,xout,yout)
        implicit real *8 (a-h,o-z)
        dimension vert1(2),vert2(2),vert3(2)
c        data ifinit/0/
c        save
c
c       map the standard triangle to the simplex
c
c
c        if( ifinit .eq. 0 ) then
c
        vert1(1)=-1
        vert1(2)=-1/sqrt(3.0d0)
        vert2(1)=1
        vert2(2)=-1/sqrt(3.0d0)
        vert3(1)=0
        vert3(2)=2/sqrt(3.0d0)
c
c        ifinit=1
c        endif
c
        xout=vert1(1)+u*(vert2(1)-vert1(1))+v*(vert3(1)-vert1(1))
        yout=vert1(2)+u*(vert2(2)-vert1(2))+v*(vert3(2)-vert1(2))
c
        return
        end
c
c
c
c
c       

